# Question: If the first n1 random variables of Exercise 8 2 have

If the first n1 random variables of Exercise 8.2 have Bernoulli distributions with the parameter θ1 and the other n2 random variables have Bernoulli distributions with the parameter θ2, show that, in the notation of Exercise 8.4,

(a) E(Θ1 – Θ2) = θ1 – θ2;

(b) var(Θ1 – Θ2) = θ1(1– θ1)/n1 + θ2(1– θ2)/n2 .

(a) E(Θ1 – Θ2) = θ1 – θ2;

(b) var(Θ1 – Θ2) = θ1(1– θ1)/n1 + θ2(1– θ2)/n2 .

## Answer to relevant Questions

Find the sampling distribution of the median for random samples of size 2m+ 1 from the population of Exercise 8.49. Use the result of Exercise 8.54 and that of part (a) of Exercise 8.52 to find the sampling distribution of R for random samples of size n from an exponential population. What is the probability of each possible sample if (a) A random sample of size n = 4 is to be drawn from a finite population of size N = 12; (b) A random sample of size n = 5 is to be drawn from a finite population of size ...A random sample of size 64 is taken from a normal population with µ = 51.4 and σ = 6.8. What is the probability that the mean of the sample will (a) Exceed 52.9; (b) Fall between 50.5 and 52.3; (c) Be less than 50.6? Consider the sequence of independent random variables X1, X2, X3, . . . having the uniform densities Use the sufficient condition of Exercise 8.7 to show that the central limit theorem holds.Post your question