A 750 ml solution is prepared by dissolving

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]

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.

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 = 2

s= 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?