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- Given an arrival process with λ = 5.0, what is the probability that an arrival occurs after t = 7 time units?Solve number 2 only3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)
- 4. Let X be a random variable with cumulative distribution function given by: F(r) = 1 – e-Az. Find the probability density function and so the expected value of variable X.With an American penny, the likelihood of getting H when it is spun on edge is 0.3. If X is the random variable where X(H ) = 1, X(T ) = −1, find the expected value E(X), the variance, Var(X), and express X in its standard form.2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1Suppose ?1, ?2, ..., ?? is a random sample fromA technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by f(y) = -10 ye 10 100 0In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: (c) E(X)= i Round your answer to two decimal places (e.g. 98.76).Prove that the events Es, E2... En are independent iff their corresponding indicator variates I,, I₂.. In are independent.NEED NEED ANSWER ASAP !!!4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON