According to a survey by a telecommunications company, the probability of a call not being connected is 5%, and the probability density function of the call time when the call is connected is ƒ(x) = }e(−¹/5)x · I(0,∞) · (I(0,∞) (x) = 1 if 0 < x and I(0,∞) (x) = 0 otherwise.) (1) The random variable X denotes the call time. Find the distribution function of X. (2) Using (1), find the moment generating function of X.

Q: (6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От OF

A: Poisson distribution is the type of discrete probability distribution. It explain the number of…

Q: 2. According to NSCB statistics, the life expectancy of Filipino women is 70.1 years. Suppose a…

A: Population mean μ=70.1, n=sample size=30, population variance σ2=4.76, sample mean x̄=72.5…

Q: Suppose X is a continuous random variable defined on (-∞, ∞) and its probability density is of the…

A:

Q: (a) Let X be a random variable with PDF ƒ(x) = 1−|x|, |x| ≤ 1. Obtain the MGF of X. (b) Find the PDF…

A:

Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

A:

Q: Find the probability that an observation taken from a standardnormal population will be more than…

A: From the provided information, The observation is taken from a standard normal population. Mean for…

Q: X and Y are independent and identically distributed random variables with ~ Exp(A). 2) Determine the…

A: Please see the next step for solution.

Q: (a) the value of k. (b) the mean and variance of X. (c) P(l£xs3).

A: According to the answering guidelines, we can answer only three subparts of a question and the rest…

Q: Let X₁, , Xn be a random sample from a large population following a uniform distribution over [0,…

A:

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: Suppose that a random variable X is an Exponential Random Variable with parameter β = 3. (a) What is…

A: Solution: From the given information, X follows an exponential distribution with parameter β=3.

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…