The joint cumulative density function of the random
geoffery mumali
Open question
2022-11-29
The joint cumulative density function of the random variables X and Y is given by:
Find the:
(i) Joint probability density function of the random variables X
and Y. [3 marks]
(ii) Marginal density function of X [3 marks]
(iii) Marginal density function of Y [3 marks]
(iv) Conditional density function of X given Y = y. [2 marks]
(v) Conditional density function of Y given X = x. [2 marks]
(vi) Are X and Y independent? [2 marks]
New Questions in Statistics and Probability
Assume that the duration of human pregnancies can be described by a Normal model with mean
267
days and standard deviation
15
days.
a) What percentage of pregnancies should last between
271
and
282
days?
b) At least how many days should the longest
25%
of all pregnancies last?
c) Suppose a certain obstetrician is currently providing prenatal care to
54
pregnant women. Let
y
represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean,
y?
Specify the model, mean, and standard deviation.
d) What's the probability that the mean duration of these patients' pregnancies will be less than
263
days?
10 samples of different pastries are on display as customers leave a bakery, they
are told that they can choose any 4 samples.
How many different selections can a customer make
if X, Y and Z are three random variables then what is the probability of (X<Y, X<Z) or what will be its probability density function
A doctor in a teaching hospital is curious to understand why some patients heal faster than others. She postulates that the patient’s age, personality, grit, and religion are the contributing factors. a. What is the outcome variable we wish to model? b. Draw the theoretical model using all the variables provided.
A stud manufacturer wants to determine the inner diameter of a certain
grade of tire. Ideally, the diameter would be 15mm.The data are as follows:
15, 16, 15, 14, 13, 15, 16, 14
(i) Find the sample mean and median.
(ii) Find the sample variance, standard deviation and range
(iii) Using the calculated statistics in parts (i) and (ii) Comment on
the quality of stud.1. A batch of 500 containers for frozen orange juice contains five that are defective. Two are selected at random without replacement from the batch.
a) What is the probability that the second one selected is defective given that the first one is defective?
What is the probability that both are defective
Determine whether each of these functions from {a, b, c, d} to itself is one-to-one.
f (a) = b, f (b) = a, f (c) = c, f (d) = d
suppose we go door to door selling candy. we consider it a success if someone buys a candy bar the probability that any given person will buy the candy bar is 0.4. What is the probability of experiencing 8 failures before a total of 5 successes.
A 750 ml solution is prepared by dissolving 414 mg of K3Fe(CN)6 (329g/mol) in sufficient water. Calculate (a) the molar analytical concentration of K3Fe(CN)6.
(b) the no. of moles of K+ ion in 50.0 ml of this solution.
An event has the probability 𝑝=38 . Find the complete binomial distribution for n=5 trails
3. Compute the probability of X successes, using Table B in Appendix A.
a. n = 2, p = 0.30, X = 1
b. n = 4, p = 0.60, X = 3
c. n = 5, p = 0.10, X = 0
d. n = 10, p = 0.40, X = 4
e. n = 12, p = 0.90, X = 2s= 2.36 n= 350 confidence level:99%
"Interns report that when deciding on where to work, career growth, salary and compensation, location and commute, and company culture and values are important factors to them. According to reports by interns to Glassdoor, the mean monthly pay of interns at Intel is $5,940. Suppose that the intern monthly pay is normally distributed, with a standard deviation of $400. What is the probability that the monthly payment of an intern at Intel is less than $5,900?”
what is the probability that exactly 15 of them would agree with the claim (or said they love insta- reels)?
Let p=0.75 for a shooter to hit a given target. The shooter wishes to shoot until the target has received 3 hits. a. What is the probability that the target will get 3 hits in 4 shots? b. What is the probability of 3 hits of the target at most 4 shots? c. What is the probability of 3 hits of the target at least 4 shots? d. What is the probability of reaching his goal with 5 bullets? e. Since the value of the target is $200 and the cost of one shot is $100, what is the expected value of the win in such a game? What is the probability distribution of the gain?
