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 thesame site is also Poisson, with mean 2 per second. Assume that thenumber of men and women are independent.a. During the next 10 seconds, what is the probability that exactly4 men visit the site? (10 points)

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

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

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

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

Suppose X and Y be random variable represents number of men andwomen who visit the site in 0 to t seconds. since it is given thatnumber of men who visit a website follows Poisson, with mean 0.296per second, and the number of women who visit thesame 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= 86400seconds, thus

d. By Poisson distribution since and that gives

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

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

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