Let X be a continuous random variable with the cumulative distribution function [0, ja x≤0 ja 05 Find the variance of random variable X. F(x) = - 25 1.

Q: True or False;  For a continuous random variable X, P(X=x) = f(x) 1. True 2.False

A: In statistics, the continuous variables are variables whose values can be given by an interval, they…

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Q: A continuous random variable X has probability distribution function f(x) , where f(x) = k(1 − x2)…

A: The k value is calculated as follows:

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Q: Q3/A/ Let X be a r.v with p.d.f f(x) =e-xl - 00 <x < oo, then the value of variance of X is -

A: Given :Let X be a r.v  with p.d.f f(x)=12e-|x|Formula : ∫-∞∞f(x)dx

Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: Of the 300 visitors polled,O liked to ski or snowboard. (Type a whole number.)

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Q: a) Let x be a random variable with distribution Fgiven by (1-e-ix Fx (x) = 0≤x≤00 otherwise Find the…

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Q: Suppose that f (x) = e-* for 0 < x Determine the mean and variance of the random variable.

A: Given problem Given that   Suppose that  f(x) = e-x for 0 &lt; x  The mean and variance of the…

Q: Let X, and X, be independent exponential distributions with the same parameter 1. What is the joint…

A: Given:  X1 &amp; X2 are independent random variables with pdfs             f(x1)=λe-λx1; x1&gt;0…

Q: A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x-x²+4) =

A: Given that E(X) = 1.5, and var(X) = 0.25 The var(X) is defined as Var(X) = E(X2) - (E(X))2

Q: 2. Suppose that a continuous random variable X has PDF f(x) = }7 (1 – x²) -1<x<1 else

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Q: Let X and Y be identically distributed with mean 4 and variance 25.(a) If X and Y are uncorrelated,…

A: a) If X and Y are uncorrelated then Cov(X,Y)=0, given V(X)=V(Y)=25 Answer(a): 50

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A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

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A: Discrete Random Variable  Two numbers are often used to summarize a probability distribution for a…

Q: Let X1,..., X, be a random sample from a two-parameter Weibull distribution with pdf x > 0 f(x) = 0,…

A: It is an important part of statistics. It is widely used.

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A: i. From the given information, the probability distribution function is f(x) = K (X2 + 20) and x=…

Q: 5.5.4. Let Y1, Y2, ..., Yn be a random sample from the uniform pdf fy(y; 0) = 1/0, 0 ≤ y ≤ 0.…

A: Step 1: Step 2: Step 3: Step 4:

Q: b) Find the variance Var(X) of X.

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Q: The lifetime of a machine part has a continuous distribution: Osxs 40 fx(x) = { (10+x)² else a.…

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Q: Suppose X₁ and X₂ have the following joint distribution X₁ 1 d 2 1/3 1/12 1/6 0 2 1/36 0 0 0 X₂ 1 0…

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Q: Let's take XI, X2 ... Хой a radom sample of distribution defined in from the uniform (0, 0+1). Is…

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Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

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Q: Random variable X has a standard normal distribution. Find the PDF of the random variable Y, where:…

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Q: Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

A: Solution

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Q: Let w₁, W2,..., wt be independent random variables from a normal distribution with mean 0 and…

A: Let w1, w2......wt be independent random variables from a normal distribution with mean 0 and…

Q: Calculate the Average and the variance

A: