KUNTAL GHOSH

2022-05-08

Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A_1, A_2, and A_3 by A_1=likes vehicle #1, A_2= likes vehicle #2, A_3=likes vehicle #3.

Suppose that

a. What is the probability that the individual likes both vehicle #1 and vehicle #2? Determine and interpret.

b. What is the probability that the individual likes either vehicle #2 or vehicle #3? Determine and interpret.

c. Are A_1 and A__2 independent events? Answer in two different ways.

d. If you learn that the individual did not like vehicle #2, what now is the probability that he/she liked at least one of the other two vehicles?

Jazz Frenia

Skilled2023-05-05Added 106 answers

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.

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)?