Let X1 and X2 be discrete random variables with joint probability distribution x1 = 1, 2; x2 = 1, 2, 3, f(x1, x2) = 10, 18 elsewhere. Find the probability distribution of the random variable Y = X1X2.

Q: Let X₁~N(-1,5), X₂~N(3,2), X3~N(0,1). They are independent rv's. Find the probability distribution…

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Q: The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a…

A: Given, The probability mass function is: 0 1 2 3 4 5 1/12 1/12 3/12 4/12…

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Suppose that two random variables Y1 and Y2 are independent, that is, for all values of Yı and y2,…

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Q: Let X be a binomial random variable with probability distribution 3-a SOOʻO**, x = 0,1, 2, 3, f(x) =…

A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

Q: X is a discrete uniform (1,3) random variable. When X=x, Y is discrete uniform (1,x). (a) Find…

A: We are given here that:P(X = 1) = P(X = 2) = P(X = 3) = 1/3 as X is a discrete uniform distribution…

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: Given that 40% of fruit flies of fruit flies posses a certain gene. So, probability that a fruit fly…

Q: A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1…

A: Given: Let X be a Poisson random variable. The probability mass function is provided as:…

Q: Let the random variable Y = a + bX. Then, µy = bux. O True O False

A: Given statement isY=a+bX

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A: If there exist two independent variables with degrees of freedom v1,v2 is the random variable of…

Q: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

Q: If X is a binomially distributed radom variable with E(X) var (X) 4/3; find the distribution of X. 2…

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Q: Find the probability of event {X ≤5.5} for a Gaussian random variable having #x Ox=2. = 3 and

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Q: Let X1 and X2 be two independent normal random variables with parameters (0,1) and (0,4)…

A: X1 and X2 are two independent normal variates  mean and variance (0,1) and (0,4) respectively. Then,…

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 24 psi.…

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Q: probability distribution of two-dimensional random variable (X,Y)

A: To calculate P(X=1|Z=0), we need to find the conditional probability that the red ball is selected…

Q: If 'b' is Constant and X be a Random Variable then VX +b)3V(X)

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Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: 40% of the fruit flies posses certain gene. So, probability that a fruit fly posses that gene = 0.4…

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: 5. Let X and Y be independent random variables such that X - exp(A) and Y ~ exp(). (a) What is the…

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

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

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Q: Let X₁, X2 be 2 mutually independent discrete random variables. The first variable X₁ can be a whole…

A: The provided information is as follows:The  and  be mutually independent discrete random…

Q: Find the joint probability function of (X,Y) where

A: Provided information is, two cards are drawn at random from a box which has 5 cards numbered 1, 2,…

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

A: Given that  Y ~ Uniform (1 , 11)

Q: d) What is the standard deviation of T? e) What is the probability that T is within 2.0 standard…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Q: Telephone calls enter a college switchboard on the average of two every three mimutes. The…

A: According to guidelines we solve first question when given questions are different.

Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

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

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Q: For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =

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Q: Let the probability distribution of random variable X be P(X= k) k! , k = 0, 1, 2, I then EX2 - ()

A: Let X has a pmf

Q: Let x1  and x1 be independent standard normal random variables. If Y1= x1 + 2x2 and  Y2 = 2x1 - x2,…

A: We know, any linear combination of normal distribution is a normal distribution. Here, x1 and x2 are…

Q: (2) (0,8)" (0,2)³-* si x = 0,1, 2, 3 fx(x) = in another case

A: Formula used.  In binomial distribution.  Expected value = E(x)= mean  E(x)= np And  Variance (x)=…

Q: Please explain your answer with steps Suppose X and Y are random variables such that E[X] = -3 and…

A: Suppose X and Y are random variables. Given: E(X) = -3 E(Y) = 6 We have to find E(X-Y). E(X-Y) =…

Q: Let the random variable X be the number of months that a certain owner of an estate needs to pay a…

A: Let Y be a random variable denoting the amount of loan. first, two months' amount is $200 received…

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

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Q: Let X be a binomially distributed random variable B(n, p) with E(X) = 2 and Var(X) = 4/3. Find n.

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Q: Let X1, X2, andX3 be independent and normally distributed random variables with E(X1) = 4, E(X2) =…

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Q: Let joint Probability distribution function of random variables X and Y be (1/3 if (x, y) = (1, 1)…

A: The joint probability distribution function for X and Y is, P(x,y)=13, if(x,y)=(1,1)13, if…

Q: If x is a random variable that has a uniform distribution in the interval [1,7].[1,7]. What is the…

A: Solution-: Let, X- be the the random variable Given: a=1, b=7 We find, P[the random variable x…