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: If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine…

A: Given: The probability generating function of a random variable X is given as:…

Q: Q2/(a) Let X be a random variable with p.d.f. 1<x<o S(x) = { find k. o.w (b) Let X be a random…

A: For the p.d.f to be valid, ∫1∞kx-2dx=1⇒k∫1∞x-2dx=1⇒k-1x1∞=1⇒k-1∞+11=1⇒k(0+1)=1⇒k=1

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

A:

Q: 6) The probability density function of the random variable X whose moment generating function () (1…

A: The moment generating function of X is given by MX(t) = (1/2)(1 + et)

Q: X is a continuous random variable having p.d.f. f(x) such that f(x) = kx2 Osxs5 otherwise Find : (a)…

A: According to our guidelines we can supported to answer only first three subparts   Given

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: The probability density function of the random variable X whose moment on () (1 + e') is: generating…

A: The MGF of X is given by MX(t) = (1/2)(1 + et)

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: An electronic product with n identical parts connected in parallel cannot function properly only if…

A:

Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: We want find  Mean= E(x) , variance = var(x)

Q: (6) Let X be a Poisson random variable with parameter 9, then E(X²) = 1.

A: Given X~Pois(θ)

Q: (30) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) = { , find E(e*) O.w

A: It is given X is a random variable with pdf f(x) = 2e-2x,0&lt;x&lt;∞0,otherwise

Q: Suppose the random variable y is a function of several independent random variables, say…

A: Given that the random variable y is a function of several independent random variables, say…

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

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: A continuous random variable has p.d.f. f(x) where { kx 0-x -1 f(x) - k(2-x) 1-x =2 otherwise Find…

A:

Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)= { find k. o.w (b) Let Xbe a random…

A: The p.d.f of X is valid if and only if ∫1∞fxdx=1⇒∫1∞kx-2dx=1⇒k∫1∞x-2dx=1⇒k…

Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)=• find k. O.w

A: The p.d.f of X is given below: fx=kx-2   1&lt;x&lt;∞0          ow

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

A:

Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

A: Given:  X has distribution function as : F(X) = 0 if X&lt;1 = k(x-1)^4 if 1&lt;X&lt;3 = 1 if X &gt;3…

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

A:

Q: X is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osxs5 otherwise Find : (a)…

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: (2) (0,8)" (0,2)³-* si x = 0,1, 2, 3 fx(x) = in another case

A: Formula used.  In binomial distribution.  Expected value = E(x)= mean  E(x)= np And  Variance (x)=…

Q: 0, x)

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

Q: 3) Find the mean and variance of the random variable X with probability function or density f(x).…

A: NOTE :  As per Bartleby instruction when more then one question is given only one has to be…

Q: Compute the joint pdf of random variables Y₁ = X₁ and Y₂ = X₂.

A:

Q: (1) Let X be a random variable with p.d.f. e 0<x<0 k ƒ(x) = < find k. O.W

A: Let X be a random variable with pdf  fx=1ke-8x        0&lt;x&lt;∞0                         otherwise…