Assignment No: 3 (Lessons 23-30)
Question 1: Marks: 4+4
Question 1: Marks: 4+4
a) The probability density function of a random variable is given as
f(x) = 2(x-1) 1<x < 2
0 Elsewhere
Calculate second moment about origin.
0 Elsewhere
Calculate second moment about origin.
b) Let x and y are two independent random variables with joint probability density function.
Find the marginal probability density function of x.
Question 2: Marks: 2+5
a) What is the probability that a poker hand of 5 cards contain exactly 2 aces?
b) A pair of dice is rolled 180 times. By using the normal approximation to binomial distribution, find the probability that a total of 7 occurs at least 25 times.
