Determine the cumulative distribution function for the random variable f (x)= 2x + 1/25 x=0, 1, 2, 3, 4.

I need help for these 4 questions.

1. Determine the cumulative distribution function for the random variable f (x)= 2x + 1/25 x=0, 1, 2, 3, 4.
2. Suppose that the random variable X has a geometric distribution with a mean of 2.5. Determine the following probabilities: (a) P(X = 1) (b) P(X = 4) (c) P(X = 5) (d) P(X ≤ 3) (e) P(X > 3)
3. Suppose that X has a Poisson distribution with a mean of 0.4. Determine the following probabilities: P(X = 0) (b) P(X ≤ 2) (c) P(X = 4) (d) P(X = 8)
4. The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random variable. Assume that on the average there are 10 calls per hour.

(a) What is the probability that there are exactly 5 calls in one

hour?

(b) What is the probability that there are 3 or fewer calls in

one hour?

(c) What is the probability that there are exactly 15 calls in two

hours?

(d) What is the probability that there are exactly 5 calls in 30

1. minutes?