Question 2: a. The probability distribution of a discrete random variable X is given below: 1 P(X =x) a If E(X)=1.5 and Var (X)=0.54, find constants a, band c.

Q: For the random variable X defined by the probability function below, answer the following questions.…

A: Given: x 2 3 4 5 6 7 f(x) 0.25 0.15 0.10 0.15 0.10 0.25

Q: IV. Find the mean of the probability distribution: X· P(X) P(X) 3/50 21/50 11/50 3/25 3/50 3 4 5…

A: Given :

Q: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

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Q: 1 A probability density function of a random variable is given by f(x)=; =- 65 expected value, the…

A: A probability density function of a random variable is given by, f(x)=165 5+ 5x  ; 25≤x≤36…

Q: Let the joint probability distribution function of two random variables X and Y be given by S…

A: Given the joint probability distribution function of two random variables X and Y as…

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A:

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A: Given that: X is a RV which follows both exponential and chi-square distributions.

Q: Question B) If the joint pdf of the continuous random variables X and Y is: fxy(x, y) = XY for 0<x<2…

A:

Q: 4.2 The probability distribution of the discrete ran- dom variable X is

A: From the given probability distribution, The sample size is 3. That is, n=3 p=1/4 Mean=n*p…

Q: *The probability function of X random variable is given as, f(x) = cx² , Dx ={-2,2,3} 1.c =? 2. P(0…

A: To find the value of c we will use the fact that the summation of f(x) over entire range is always…

Q: Question 4 Let X be a continuous random variable such that P(X 6): P(X> 6) = (Round the answer to 2…

A: P(X&lt;6)=0.1

Q: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

A:

Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: Suppose x is a random variable best described by a uniform probability distribution with c= 15 and d…

A: Given: X  is a random variable best described  by  Uniform  probability distribution with c= 15 and…

Q: b) The probability density function of random variable X is given as: S(x) = {4 - Bx if 0 <x<1…

A:

Q: Question 4. The random variables X and Y have the joint pdf given by fxy(r, y) = e*, I> 0, 0 < y <…

A: We have given that  The random variables X and Y have the joint pdf given by fXY(x, y) = e-x.…

Q: A simple random sample X1, …, Xn is drawn from a population, and the quantities ln X1, …, ln Xn are…

A: Solution: From the given information, a simple random sample  is drawn from a population and Q-Q…

Q: Let X and Y have a bivaraite gamma distribution of Kibble with parameters a = 1 and 0<0< 1. What is…

A:

Q: Ex. 2. A random variable X is exponentially distributed with the deviance 1/4. Compute the…

A:

Q: If a discrete random variable has the probability mass function, ?(?)={ 1/6    ?=1            1/3…

A: The cumulative distribution function is:F(x)=0, x&lt;116, 1≤x&lt;416+13=12, 4≤x&lt;612+13=56,…

Q: 3. Let X and Y be two Binary random variables with joint probability distribution: x = 0 x = 1 0.2…

A: The joint probability density function is given as- fx,y x=0 x=1 y=0 0.2 0.4 y=1 0.1 0.3

Q: Pls explain to me step by step and dont skip any steps. Thanks

A: To locate and analyze the critical points of the given non-linear system

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A: Step 1: Given table, pdf tablex01234P(X = x)0.150.3a0.20.1 Step 2: a) The value of 'a' can be…

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Q: The probability distribution of a discrete random variable X is given in Table Q3. Table Q3 1 x 2…

A:

Q: Q2 Suppose Y is a discrete random variable such that P(Y= y) = K(1-a)-1,0 < a <1 for y = 1,2,... co.…

A: P(Y=y)=k(1-a)y-1 ; y=1,2,...

Q: The pdf of a random variable X is given by K fx (x) =- a<x<b otherwise where K is a constant. (i)…

A:

Q: If a random variable follows a Poisson distribution and if: 4P(x=0)=P(x=1), then find E(x² ) Select…

A: For a poisson distribution  EX2=λ2+λ

Q: Suppose a discrete random v mass function (where c> 0 is a constant): 1 5c p(w) 2c

A: According to the sum, a) We know, ∑w=04p(w)=1 So, 2c+5c/4+c/2+c/4=1 Or,4c=1 Or, c=1/4 The value os…

Q: Example 24: Let X is a normal random variable denoted by N (0, ơ). Let Y=X*. Find the expected value…

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Q: In which probability distribution would a random variable XX have E(X)=λE(X)=λ?

A: