Statistics and Probability Answers

 Let X and Y be two independent random variables having joint probability density function f(x, y) = 1/ 2πσ2 e − (x−µ) 2 σ2 e − (y−µ) 2 σ2 − ∞ < x, y < ∞

Find the moment generating function of Z = X+Y 2 and hence the mean and variance of Z

 A discrete random variable X has probability distribution function f(x) = 12! /x!(12−x)!p x (1 − p) 12−x x = 0, 1, 2, .., 12 0, elsewhere

(i) if p = 0.3, find Pr(X > 3).

(ii) find possible values of p if Var[X] is equal to 1.92. 

 Let A and B be two events defined on a sample space S. If Pr(A)=0.8; Pr(A| B )=0.85 and Pr(A| B^ c )=0.75; determine the probability that neither of the two events occur.

The scores of individual students on a national test have a normal distribution with mean 18.6 and standard deviation 5.9. At Bagabag National High School, 76 students took the test. If the scores at this school have the same distribution as national scores, what are the mean and standard deviation of the sample mean for 76 students?

A population of 1,000 students has an average weekly allowance of μ = 350 Php and standard deviation of σ = 56.13 Php. What is the probability that a random sample of size n = 30 will have an average weekly allowance between 335 and 360 Php?

Calculate the mean and the variance of the discrete random variable x which one values 12 and 3, given that P(1)=10/33, P(2)=1/3 and P(3)=12/33

the mean score and the standard score in the statistics test are repectively equal to 80 and 2.5, whereas in the pre calculus test they are respectively equal to 70 and 2. if vince got a score of 85 in statistics and a score of 75 in pre-calculus, in which subject is her standing better assuming normality on both subject?

A box contain 10 black marble, 8 white marble and 6 yellow marble. If a ball is drawn at random, what is the probability of getting black marble and white marble?

A food manufacturing company produces oatmeal cookies that have a sugar content that

is approximately normally distributed. The mean sugar content is 1.1 grams with a standard

deviation of 0.15 gram. Determine the probability that a random sample of 10 oatmeal cookies

will have an average sugar content of greater than 1.2 grams.

Each time Caroline goes shopping she decides whether or not to buy fruit.

The probability that she does buy fruit is 0.4.

Independently, she then decides whether or not to buy a CD, with a probability of 0.3 that she does buy a CD.

Work out the probability that she buys fruit or buys a CD or both.