4. Assume that X is a continuous random variable with cumula- tive distribution function (cdf) if x < -3 0.3V +3 if -3 5. (a) Compute P(-2< X < 3). (b) Find the median of the distribution of X.

Q: Let X be a binomial random variable with probability distribution 3-a SOOʻO**, x = 0,1, 2, 3, f(x) =…

A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

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A:

Q: F(x)={5(x-5)(9-x²):25r54 (x-5)(9-x² ):2<x<4 elsew here Calculate P x =- and Psxs (b) SHOW that the…

A: 1st question is wrong. For other we apply binomial theorem.

Q: d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X =…

A: Given problem Given that   d)   The random variable X has a Poisson distribution such that P( X=0…

Q: A) Suppose that X is a random variable with if 0 < x < 2 fx(x) = otherwise

A: We have to find the var(x)  Using formula  Var(x) = E(x^2) - [E(x)]^2

Q: (1)A random variable is defined as 1/36(2x-1); x= 1,2,3,4,5,6     (a)Construct the Probability…

A: Random variable  X defined  as  fx=1362x-1   x=1,2,3,4,5,6∴fi=PX=xi         x1=1, x2=2,x3=3…

Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

A:

Q: 9. Let X be a normally distributed random variable with a mean equal to 2 and a variance equal to 9.…

A: The last statement ( i.e. "E") Var(3X-2)=25 is incorrect one.

Q: Let X₁, X2, ..., XK-1 have a multinomial distribution. (a) Find the mgf of X₁, X₂, ..., XK-2. (b)…

A:

Q: n F. De X(w) i- -X(w)

A: the distribution function is also known as a cumulative distribution function.shows that the…

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A: At first   write the distribution of sum of the two independent Poisson variable..........

Q: Let T t(7), then the distribution of T is distribution.

A: Given,  T~t(7)

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A:

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: 5. An automobile dealer has found that X, the number of cars customers buy each week, follows the…

A: The given function is: f(x)=kx2x!,x=1,2,3,40,       Otherwise

Q: EXERCISE 4. Suppose that X is a continuous random variable whose probability distribution function…

A: a) The value of c is calculated as follows: ∫02c4x-2x2dx=1c4x22-2x3302=1c8-163=1c=38

Q: If a procedure meets all the conditions of a binomial distribution except that the number of trials…

A: We want to find probability  X~Geometric(p=0.25) P(4)

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: (a) P(2 < Xs 5), (b) P(3 < X s 7), and (c) P(X 2 6). *

A:

Q: F(0) 1/2 1/3 1/3 1/2 Consider the above distribution function for a random variable X(0) a) P(X s…

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

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Q: Suppose that the random variableX has the continuous uniform distribution í 1,0 < x < 1 0, otherwise…

A: Given that: The probability density function of random variable X is given as: fx=1,   0≤x≤10,…

Q: 2) Suppose that X is a continuous random variable with probability distribution fx(x) = ₁ 0 ≤x≤4…

A: The probability distribution function (pdf) of a continuous random variable X is

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A:

Q: 1. Let X, 2 Poisson(A,), for i = 1,2. (a) Show that X1 + X2~ Poisson(A1 + Ag). (b) Show that X| X +…

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Q: 1. Let X, 2 Poisson(A,), for i = 1,2. (a) Show that X1 + Xy~ Poisson(A + A2). (b) Show that X| X + Y…

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Q: The probability that a rose bud blooms is p. In a random sample of 500 rose buds, 240 of them…

A: Given that, Sample size n=500 Sample proportion of rosebuds that bloomed p^=240500=0.48

Q: Find Var(X) if X is a Uniformly distributed b Binomially distributed C Normally distributed

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A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…