X is a binomial random variable with the probability of succ

X is a binomial random variable with the probability of success = 0.52 and the number of trials = 48. Calculate E(X) to two decimal places.

X is a continuous random variable with cumulative distribution function F(x). If F(0) = 0.138, F(2) = 0.233, and F(5) = 0.837, what is the probability that X > 5? Calculate your result rounded to three decimal places.

Solution

a)

For a binominal random variable,

E(X) = n p = 48*0.52 = 24.96 [answer]

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b)

Note that

P(x>5) = 1 - P(x<5)

As

P(x<5) = F(5) = 0.837,

P(x>5) = 0.163 [answer]