A continous random variable x has p.d.f.,then a. f(x) >=1 b. f(x) >==0 O C. 0=;0

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

Q: Problem 2. Let X1,..., X, be any n random variables such that |Cov(X;, X;)| < 0, i, j 1,..., n. Let…

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Q: 7. Calculate the variance of g (X) = 2X + 3, where X is a random variable with probability…

A: The given data is as follows: x0123f(x)

Q: 1. (a) A continuous random variable X has a p. d. f. f(x) = 3x?, 0 a) and (ii)P(X > b) = 0.5. (b)…

A: 1). a). Given P.D.F is: fx=3x2 : 0≤x≤1 i). For PX≤a=PX&gt;a…

Q: Let X1, X2,... be independent Exponential (3) random variables and Z = } E=1 X;. If Mz (t) is the…

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Q: A nature reserve has one bird of an uncommon species which frequents the large expanse of reed beds…

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Q: (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20 ≤ ≤ 30 (e)…

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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: Q3. The moment generating function for a random variable X is e3t M(t)=1-t2¹ What are the mean and…

A: The moment generating functionMx(t)=e3t/(1-t2)    -1&lt;t&lt;1To find mean and variance of X Concept…

Q: A random variable, x, has p.d.f. f (x) given by f (x) = 1 а. always equals 1 b. 0 < x< 1 C. Not…

A: We know that,  If a random variable x having probability density function f(x) by the property of…

Q: 3. Let the random variable X have the pmf f(x) = = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² for x =…

A: The provided information is as follows:The probability mass function of  is .

Q: Given that the random viriable X has mean µ = 90 and SD e= 15, find the mean and SD of each of the…

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Q: . Let Y be a continuous random variable where f(y) F(y)? (a) Y 18 Y 15 Y-3 18 y+3 (b) (c) (d) 18 (e)…

A: The random variable Y is a continuous random variable with pdf f(y) = 1/18 ; -3 ≤ y ≤ 15

Q: 1) Find the Mean and Variance for the following function [1 -x, 0sxs1 1 (10 – x), 1sxs 10 45 f(x) =…

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Q: (42) Let X be a random variable with p.d.f. ke 0<x<0 f(x) ={ find k. O.W

A: Given : f(x)=ke-23x                    0&lt;x&lt;∞

Q: 4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the…

A: Option (I) is correct as E(X2)&gt;= (E(X))2 when we find Variance.

Q: (33) Let X be a random variable with p.d.f. e2k x= 1,2,3 f(x)=- find (1) k (2) E(x+1) O.W

A: Given that X is a random variable with p.d.f f(x)=e2k ; x=1,2,30     ; Otherwise.

Q: A continous random variable x has p.d.f.,then a. f(x)>=1 b. f(x)>==0 C. d. f(x) >:0 0=<lt; f(x)=<1

A: It is given that f(x) is a probability density function (pdf) of a random variable X.

Q: (5) Let X be a random variable with p.d.f. k 1<x<o 2 f(x) =< , find k. O.w

A: Given: fx=kx2            1&lt;x&lt;∞0                 Otherwise

Q: Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ = EX?…

A: Given : X be the random variable  Y=aX

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

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Q: Then find E[X], E[X2], E[2X+5], E[(X+1)²].

A: Solution - Given that X be a uniform random variable with pdf  f(x)=0.10   -5&lt;=X&lt;=5 Find E(X)…

Q: 20) Let X be a random variable with p.d.f. k T<x<10 f(x) =- , find k. O.w

A: Solution: Let X be the random variable with pdf f(x) is  f(x)=kx       1&lt;x&lt;100      otherwise

Q: 48) Let X be a random variable with p.d.f. 1 -8x 0<x<00 k f(x)= , find k. O.w

A:

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: Let X, Y N (2, 3) two normal random variables with mean 2 and variance 3. Which of the following…

A: Normal distribution  mean , median and mode are eqaul

Q: -2 kx 1<x<0

A: The probability density function given is, fx=12kx-2 , 1&lt;x&lt;∞0 , o.w Here X is the random…

Q: The joint p.m.f of (X,Y) is given by P(x, y) = 2x + 3y), x =,1,;02y = ,13,.2.Find the marginal…

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Q: If X Z N(5,4), then what is the probability that 8 < Y < 13 where Y = 2r +1?

A: Solution: Let X~N(μ= 5, σ2= 4)

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: 8. IFX is a continuous random variable and y = ax + b then the expected valued of y = ? a. aE(x) b.…

A: y=ax+b

Q: Let X be a random variable having p.d.f. fx(x) = cx², -2 < x < 2. For the following parts, your…

A: Given density function: fx=cx2, -2&lt;x&lt;2 c value: ∫-22fxdx=1 from the total probability…

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

A: Given, X be a random variable with p. d. f. f(x)=12kx-2   ; 1&lt;x&lt;∞0           ; O.W. constant k…

Q: If the variance of X is 0 then the covariance between X and Y

A: Lets analyze the question.

Q: (7) Let X be a random variable with p.d.f. 1<x<0 f(x) = { ,find k. O.W

A: Reviewing information, X is a r.v. with pdf,f(x)=kx-2                          1&lt;x&lt;∞0…

Q: If the probability den sity function of a continu ous random variable X is [a+ ba² 0<x <1 f(x) :…

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Q: Q2. Let X be a random variable with (a) Find E(X) (b) Find M(t). (0.42 f(x)=0.46 0.12 if x=0 if x =…

A: The random variable X f(x)=0.42         If x=0       0.46          If x=1      0.12          If…