Problem 5: It is known that 5% of men are color blind.\" ) What is the probabili
ID: 2945741 • Letter: P
Question
Problem 5: It is known that 5% of men are color blind." ) What is the probability, that out of 2000 randomly chosen men, exactly 50 would be color blind? (i) Estimate this answer by using the Poisson approximation. Problem 6: Let X,Y be independent random variables on a sample space such that, X ~ Poisson(1) and Y~Bernoulli(0.5) Determine: (i) E[2X-3Y] (ii) Var(2X-3Y) (iii) P(X+Y = 2) (iv) EX2] Problem 7: Three fair coins are fipped. Let X be the number of heads. Let Y be equal to 1 if all coins land the same outcome, i.e. HHH or TTT, and 0 if otherwise. Calculate Cov(X,Y).Explanation / Answer
Ans-7.
CovX,Y=E[XY]?E[X]E[Y]
We have 8 outcomes.
HHH ?XY=3 for all other combinations XY=0
E[XY]=3/8
E[X]=3/2,E[Y]=1/4
E[XY]?E[X]E[Y]=0=cov(X,Y)