Let Y be a discrete random variable with probability mass function (pmf), p (y). The mean of Y can be found by

Q: Let X1, X2, ..Xn be a random sample of size n from a distribution with a probability density…

A: To find MLE of B, We find L then we diff. it with respect to B  Then we put it equal to zero.  And…

Q: If the probability density function of the random variable X is x>0, f(x)= 0, Otherwise. Then the…

A: Given data :  f(x)=e-x , x>0 0 , otherwise Finding Mean ,…

Q: Show that the following function is a valid probability mass function of the random variable X.…

A: Sol

Q: The joint pdf of X and Y is (i) ||-|x|-° fx.x (x, y) =-e Are X and Y statistically independent…

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Q: If X is an exponential random variable with parameter 1 = 1, compute the probability density…

A: Solution

Q: Let X be a continuous random variable with PDF 2x 0 < x < 1 fx(x) = {0 otherwise Find the expected…

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Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

A: We have to check whether the probability diatribution is valid or not.  For valid probability…

Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

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Q: Consider a random variable X whose probability mass function is given by 0.1 x = -3 r = 0 I = 2.2 x…

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: Find the characteristic function of a uniformly distributed random variable X in the range [0,1] and…

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Q: If X is an exponential random variable with parameter 1 = 1, compute the probability density…

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Q: Let X be a random variable whose probability density function is given by -2kx f(x) = +-e-kr x > 0…

A: Given that k=0.75 And the probability density function is, f(x)=e-2*0.75x+12e-0.75x, x&gt;0…

Q: Find the variance of the probability density function using two methods. 5 f(x) 8 [0, 2]

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Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

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

Q: Show that the following function is a valid probability mass function of the random variable X. p(x)…

A: Each probability mass function p(x) satisfies following two conditions: p(x)&gt;=0, for all…

Q: andom variable

A: The cumulative function is given as, fxx=10.5821-x2  , -0.3≤x≤0.30      ,       O.W. The probability…

Q: If the random variable X · Exp(0), then what is the probability density ction of the random variable…

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Q: Let X be a continuous random variable with probability density function given by ƒ(x)=Kx³ if x21,…

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Q: 1. Let X be a random variable with probability density function f(x) = {k(4 – x²) -2<x<2 otherwise…

A: #1     X   be a random variable with pdf                      f(x)  = k(4-x2)      -2 &lt; x &lt; 20…

Q: Let Xo, X1, X2, ... be independent random variables such that X, has an exponential distribution…

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Q: The probability mass function of a discrete random variable X is defined as p(x) = x/10 for x =…

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Q: Calculate the mean and variance of the random variable y, whose probability mass function is: f(y) =…

A: Farmula used E(Y)=∑YP(Y=y) Variance=V(Y)=E(Y2)-(E(Y))2

Q: Suppose that X is a discrete random variable with the probability mass function given by: P where i…

A: Given, X is a discrete random variable with a probability mass function- x 1 2 3 4 5 6 7 8 P(x)…

Q: Let X be a discrete random variable with probability mass function P(X= x) = p(1 −p)^x ; x=…

A: Given that, X be a discrete random variable with probability mass function P(X= x) = p(1 −p)x      ;…

Q: The random variables U1 and U2 are independent, and each has an exponential distrib with rate…

A: From the given information, U1 and U2 are independent and each has an exponential distribution with…

Q: Let X be a continuous random variable whose probability density function is: f (x) = 3x² for 0 <x <…

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Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

Q: Let Y be a continuous random variable with a probability mass function: - = r· | Derive the moment…

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Q: If X has an exponential distribution with probability mass function Sle-Ax, f(x) = P(X = x) = {de, x…

A: Solution-: We have, The probability mass function of X is,  f(x)=P(X=x)=λ*e-λ*x       ;x≥0…

Q: Let X and Y be two discrete random variables with joint probability mass function Pxy (x, y). Show…

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Q: Suppose that X is a discrete random variable with the following probability mass function where…

A: From the given information, the random variable X is, X 0 1 2 3 P(X) 2θ/3 θ/3 2(1-θ)/3 (1-θ)/3…

Q: Suppose that X is a random variable with probability density function given by: fx (x) = { k(x³ +…

A: To find k k∫02(x3+x) =1kx44+x2202 =1k164+42 =1k=16

Q: Let X be an exponential random variable with the following probability density functioi x20 f(x;2)={…

A: Solution: Let X be an exponential random variable having probability density function…

Q: Let X be a discrete random variable with expectation -0.5 and variance 3. Let Y=−2X+8, find the…

A: The expectation and variance of discrete random variable X are -0.5 and 3, respectively.

Q: find the probabilities that a random variable having this probability density will take on a value…

A: Based on given probability density function, we have to find the probabilities P(0.2 &lt; X &lt;…

Q: The probability density function of a continuous random variable X is given by F(2) = {*(=* = k(x² –…

A:

Q: The probability mass function of a discrete random variable X is given as: (x² +5x) x = 1,2 f(x)%3=…

A: Solution: From the given information, the probability mass function of X is

Q: Let Yi and Y2 be independent Poisson random variable with means , and 22, respectively. Using a…

A: Given that : Let Y1, Y2 be independent Poisson random variables with means X1 and X2, respectively.

Q: Find the moment generating function, mean and variance of X if the probability mass function is f(x)…

A: Let X be a random variable with probability function (probability mass function or probability…

Q: Let Z be a random variable given by Z -+ 4Y where X and Y are two independent random variables with…

A: From the given information, fXx=1aux-ux-10fYy=1bux+10-ux-10 The above density can be written as,…

Q: Let X1, X2, ..., Xn be a sequence of independent and identically distributed random variables having…

A: Let X1, X2,...,Xn be a sequence of independent and identically distributed random variable having…

Q: Let X be a Poisson random variable with parameter 1> 0. (a) Calculate EX, EX(X – 1) and EX(X – 1)(X…

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Q: Let X be a continuous random variable with probability density function 1 fx(x) = -1 1/4) is

A: P(X2&gt;1/4)=1/2 (e).

Q: b. Let X and Y be discrete random variables with joint probability function, f as follows, Y = 0 Y =…

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Q: Let Y be a discrete random variable.  Let c be a constant.   PROVE  Var (Y) = E (Y2) - E (Y)2

A: We have to deduce the formula of variance.

Q: The expected values of the independent random variables x and y (E(x) and E(y)) for a joint density…

A: Given: E(x)=5 E(y)=6   x and y are independent random variable

Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X +…

A: 1] X is a normal random variable 2] μ=5 and σ=1 3] Y=X2-10X+25