If E and F mutually explusive, then \(P(E or F=P)(E)+P(F)=0.25+0.45=0.7\)

Question

asked 2020-12-28

An experiment on the probability is carried out, in which the sample space of the experiment is

\(S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.\)

Let event \(E={2, 3, 4, 5, 6, 7}, event\)

\(F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}\).

Assume that each outcome is equally likely. List the outcome s in For G.

Now find P( For G) by counting the number of outcomes in For G.

Determine P (For G ) using the General Addition Rule.

\(S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.\)

Let event \(E={2, 3, 4, 5, 6, 7}, event\)

\(F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}\).

Assume that each outcome is equally likely. List the outcome s in For G.

Now find P( For G) by counting the number of outcomes in For G.

Determine P (For G ) using the General Addition Rule.

asked 2020-10-28

Let's calculate the following exponential probability density function.

\(f(x) = \frac{1}{8} e^{x/8} for x \geq 0\)

a.Find \(P(x \leq 4)\)

b.Find \(P(x \leq 6)\)

с.Find \(P(x \geq 6)\)

d.Find \(P(4 \leq x \leq 6)\)

\(f(x) = \frac{1}{8} e^{x/8} for x \geq 0\)

a.Find \(P(x \leq 4)\)

b.Find \(P(x \leq 6)\)

с.Find \(P(x \geq 6)\)

d.Find \(P(4 \leq x \leq 6)\)

asked 2021-01-19

If P(A)=0.5, P(B)=0.4, and A and B are mutually exclusive, Find P(A or B). P(A or B)=____

asked 2020-12-16

c. Let \(f(x) = \frac{e^{x}-e^{-x}}{x}\).

The actual values values is \(f(0.1) = 2.003335000\). Find the relative error for the values obtained in parts (b) and (c)

The actual values values is \(f(0.1) = 2.003335000\). Find the relative error for the values obtained in parts (b) and (c)

asked 2020-12-09

Determine whether the following state-ments are true and give an explanation or counterexample.

a) All polynomials are rational functions, but not all rational functions are polynomials.

b) If f is a linear polynomial, then \(\displaystyle{f}\times{f}\) is a quadratic polynomial.

c) If f and g are polynomials, then the degrees of \(\displaystyle{f}\times{g}\) and \(\displaystyle{g}\times{f}\) are equal.

d) To graph \(\displaystyle{g{{\left({x}\right)}}}={f{{\left({x}+{2}\right)}}}\), shift the graph of f 2 units to the right.

a) All polynomials are rational functions, but not all rational functions are polynomials.

b) If f is a linear polynomial, then \(\displaystyle{f}\times{f}\) is a quadratic polynomial.

c) If f and g are polynomials, then the degrees of \(\displaystyle{f}\times{g}\) and \(\displaystyle{g}\times{f}\) are equal.

d) To graph \(\displaystyle{g{{\left({x}\right)}}}={f{{\left({x}+{2}\right)}}}\), shift the graph of f 2 units to the right.

asked 2020-11-09

The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male and event B: student has blue eyes.

\(\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&&&10\\ \text{Brown}&&&40\\ \hline \text{Total}&20&30&50 \end{array}\\)

Copy and complete the two-way table so that events A and B are mutually exclusive.

\(\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&&&10\\ \text{Brown}&&&40\\ \hline \text{Total}&20&30&50 \end{array}\\)

Copy and complete the two-way table so that events A and B are mutually exclusive.

asked 2020-12-29

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

\(PP( \text{high-quality oil})=.50 P(\text{medium-quality oil} )=.20 P( \text{no oil} )=.30\)

a. What is the probability of finding oil?

b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test follow.

\(P( \text{soil | high-quality oil} )=.20 P( \text{soil | medium-quality oil})=.80 P( \text{soil | no oil})=.20\)

How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

\(PP( \text{high-quality oil})=.50 P(\text{medium-quality oil} )=.20 P( \text{no oil} )=.30\)

a. What is the probability of finding oil?

b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test follow.

\(P( \text{soil | high-quality oil} )=.20 P( \text{soil | medium-quality oil})=.80 P( \text{soil | no oil})=.20\)

How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

asked 2021-01-07

a. Let \(f(x) = \frac{e^{x}-e^{-x}}{x}\)

\(\text{Find} \lim_{x \rightarrow 0}(e^{x}-e^{-x})/x\)

\(\text{Find} \lim_{x \rightarrow 0}(e^{x}-e^{-x})/x\)

asked 2021-02-20

Indicate whether the expression defines a polynomial function.
\(\displaystyle{P}{\left({x}\right)}=−{x}{2}+{3}{x}+{3}\)
polynomial or not a polynomial
If it is a polynomial function, identify the following. (If it is not a polynomial function, enter DNE for all three answers.)
(a) Identify the leading coefficient.
(b) Identify the constant term.
(c) State the degree.

asked 2021-01-17

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of \(25^{\circ}F\). However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to \(25^{\circ}F\). One frozen food case was equipped with the new thermostat, and a random sample of 21 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a \(5\%\) level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)

(a) What is the level of significance?

State the null and alternate hypotheses.

\(H0:?_{1}^{2}=?_{2}^{2},H1:?_{1}^{2}>?_{2}^{2}H0:?_{1}^{2}=?_{2}^{2},H1:?_{1}^{2}\neq?_{2}^{2}H0:?_{1}^{2}=?_{2}^{2},H1:?_{1}^{2}?_{2}^{2},H1:?_{1}^{2}=?_{2}^{2}\)

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

\(df_{N} = ?\)

\(df_{D} = ?\)

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.

(a) What is the level of significance?

State the null and alternate hypotheses.

\(H0:?_{1}^{2}=?_{2}^{2},H1:?_{1}^{2}>?_{2}^{2}H0:?_{1}^{2}=?_{2}^{2},H1:?_{1}^{2}\neq?_{2}^{2}H0:?_{1}^{2}=?_{2}^{2},H1:?_{1}^{2}?_{2}^{2},H1:?_{1}^{2}=?_{2}^{2}\)

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

\(df_{N} = ?\)

\(df_{D} = ?\)

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.