Question

(Text answers preferred)

Suppose that the number of men who visit a website is Poisson, with mean 0.296 per second, and the number of women who visit the same site is also Poisson, with mean 2 per second. Assume that the number of men and women are independent.

a. During the next 10 seconds, what is the probability that exactly 4 men visit the site? (10 points)

b. During the next 5 seconds, what is the probability that at least 1 man visits the site? (10 points)

c. What is the expected number of the number of men who visit the site in one day? (10 points)

d. What is the standard deviation of the number of men who visit the site in one week? (10 points)

e. During the next 15 seconds, what is the probability that 1 man and 2 women visit the site? (10 points)

Answer 1

Suppose X and Y be random variable represents number of men and women who visit the site in 0 to t seconds. since it is given that number of men who visit a website follows Poisson, with mean 0.296 per second, and the number of women who visit the same site is also Poisson, with mean 2 per second, for next t seconds

, Thus

a. Here t=10 sec and we have to obtain P(X= 4)

b. Here t= 5 sec and we have to obtain

c. Since by poisson distribution and here we have time as one day means 24 hours or 24*60*60= 86400 seconds, thus

d. By Poisson distribution since and that gives

Here t= one week means 7 days of 7*86400 = 604800 secods thus

e. Here we have to find for t= 15 sec, P(X=1, Y=2). Since X and Y are independent, thus