2Y 0 Show that has a x² distribution with 2 degrees of freedom.

Q: Suppose X has a continuous uniform distribution over the interval -1,1. Determine the variance.…

A: GivenX has a continuos uniform distribution over the interval (-1,1)The corresponding density…

Q: Derive the variance of the Student's t distribution using the definition Var (X) = ELX²] - Ex)²

A: t distribution: Let us assume X is a random variable following standard normal distribution and Y is…

Q: Show that the t-distribution with r = 1 degree of freedom and the Cauchydistribution are the same.

A: We have to prove that the t distribution with r=1 degree of freedom and the Cauchy distribution are…

Q: Select all distributions which are approximately symmetric.

A: Here given 6 different dot plot for data .

Q: Show the derivation of the PDF of the student's T-Distribution. Show complete solution.

A: Drive the pdf of student's t distribution

Q: (2 cos z-sin z)² dx Evaluate sin z

A:

Q: If Y Poisson(2) and Z Poisson(3) are independent, what is distribution of W = Y + Z?

A: Solution: Given  Y~Poisson(2)    and  Z~Poisson(3)   Y and Z are independent random variable

Q: Let ZZ be a discrete random variable taking one of the four distributions covered in Chapter 10.…

A:

Q: f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the…

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Q: If X~beta(3,2) is independent of Y~beta(3,4), what is the distribution of X+Y

A: The objective of this question is to find the distribution of the sum of two independent random…

Q: Let X be a random variable representing the number of times that you have to roll two dice until you…

A: Here, the given context follows negative binomial distribution with k = 10 and p = 118 (probability…

Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k

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Q: Let X~ Normal(2, 1) and Y = 2X-3. What is the distribution of Y? a. There is insufficient…

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Q: (Y-1)². Use one decimal place accuracy.

A: Given that  Y ~ Uniform (1 , 11)

Q: When can we apply t-distribution?

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Q: distributions of both Y1 and Yn are uniform and continuous

A: We know that first order statistic PDF is given by fy1(y1) as shown below. Mean or Expected value…

Q: X and Y be standard normal random variables with correlation ρ. Compute the joint and marginal…

A:

Q: Let X follow normal distribution with mean 50 and standard deviation 4. Let Y follow uniform…

A: Let's see first theoretically, X~N(50,4)Y~N(20,35) Then the value of…

Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: 1.28 On any day, the number of accidents on the highway has a Poisson distribution with parameter A.…

A: We  have to find mean and standard deviation for given uniform distribution...

Q: When do we use a mean and SD to define a continuous variable distribution?

A: Given information: For a continuous variable distribution with specified mean and standard…

Q: fx(x) 4 a -1a

A: We have to find the value of constant for valid pdf.

Q: EZ = X +Y if X,Y are

A: X follows normal distribution with mean 0 and variance 1. Y follows normal distribution with mean 0…

Q: If X is a random variable with any continuous distribution, explain why P(X<x)=P(X≤ x)

A: The concept of probability is an essential tool in many fields, including statistics, economics, and…

Q: What is the distribution of X + Y when X and Y are independent random variables with uniform…

A: The objective of the question is to find the distribution of the sum of two independent random…

Q: X and Y be standard normal random variables with correlation p. Compute the joint and marginal…

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Q: The time to fly between New York City Chicago is uniformly distributed with a minimum of 120 minutes…

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Q: The probability distribution of the discrete random variable X is 3-x x = 0,1,2,3. .4, Find the…

A: Solution-: We have the p.m.f. of X is given by,  f(x)=3x*(14)x*(34)3-x f  ;  x=0,1,2,3;   We find…

Q: Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

A: The geometric distribution and Poisson distribution are two different types of probability…

Q: Suppose data x is distributed with poisson distribution with λ=100 then find the probability of x=99

A: The random variable is given here which follows the Poisson distribution with parameter . is 100The…

Q: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

A: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

Q: Suppose Y is a continuous random variable with uniform distribution having mean 1 and 4 What is P(Y…

A: