Suppose X is a discrete random variable with finite first and second moments. Show that E (x -)E(x-A) for all b E R.

Q: Let X, Y be independent Uniform (0, 2) random variables. Define Y, if X }. Z = Compute E[Z] and…

A: X,Y ~ Uniform(0,2) E(X) = E(Y) = 0+22=1 Var(X) = Var(Y) = (2-0)212=412=13 Z = Yif X <122Yif X≥12…

Q: Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2)…

A: Suppose that X , Y and Z are statistically independent random variables ~ X2(2) distribution . U = X…

Q: X is a discrete random variable and takes the values 0,1 and 2 with probabilities of 1/6, 1/3 and…

A: Moment generating function:

Q: Suppose for a certain random variable, X, we have V( X) =1. then which of the following is a true…

A: For a certain random variable, X, we have V(X)=1.

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X 1/9 1/9 -1 1…

A: There are two type of variable, they are dependent and independent variable. Dependent variable is…

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: Let X be a random variable representing a risk with E(X) = 10 and E(X²) = 125. A portfolio contains…

A:

Q: Suppose that Y ~ Normal(0, 1) and define new random variable X by X=Y². Compute ELYI

A: Given that Y~Normal0,1 Here, E(Y)=0V(Y)=1⇒E(Y2)-EY2=1⇒E(Y2)-0=1⇒E(Y2)=1

Q: Given p1 and p2 be positive real numbers less than 1 and let X and Y be discrete random variables…

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

Q: Let X be a random variable with E (X") = 0.8 for n = 1,2,3, . , 00 the moment generating function of…

A: Given: X be a random variable with EXn=0.8  for all  n=1,2,3.....∞ we need to find the Moment…

Q: Suppose that we observe m iid Bernoulli(0) random variables, denoted by Y₁,..., Ym. Show that the…

A:

Q: Suppose that P{X = a} = p, P{X = b} = 1 – p, X-b a. Show that а-b is a Bernoulli random variable b.…

A: Given: P {X=a} = p,  P {X=b} = 1-p To Proof/ Find: a. x-ba-b is a Bernoulli random variable b.…

Q: Let X be a random variable with PDF fx(x) = x > 0, %3D DDR

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

Q: Suppose that the time (in hours) required to repair a machine is an exponentially distributed random…

A: The probability density function of exponential distribution is given by

Q: Let X be a binomial random variable with parametern=3, p-0.2 then find P(X -0) 0.513 O 0.512 O 0.411…

A: The binomial formula is: This is the case of binomial, as there are only two possible outcomes…

Q: Suppose X₁ and X₂ are Find UMVUE for μ independent N(μ, 1) random variables, for an unknown…

A: Given Xi~N(μ,1), i=1,2

Q: The characteristic function for a Gaussian random variable X, having a mean value of zero, is ¢, (@)…

A:

Q: A sample of size 200 is taken at random from an infinite population. Given that the population…

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Q: Suppose two independent random variables X1~ uniform[0,2a] and X2 - uniform[0, 2b]. Moreover, an…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0 ≤ x ≤ 1. Find…

A: Solution (2) There is two different questions So i am solving first

Q: Suppose an insect lays a very large number of eggs Y, where Y ~ Po(lambda), and suppose that each…

A: Introduction: The random variable Y denotes the number of eggs laid by a randomly chosen insect. It…

Q: Let X be a discrete random variable with PMF: (0.33 for k = 0 0.27 for k = 1 | 0.15 for k = 2 Px(k)…

A: From the given information, X be a discrete random variable with PMF, PXk=0.33 for k=00.27 for…

Q: Let X, X,...X, be 'n' random variable which are identically distributed such that Xg= 1 with a prob.…

A: Given that   Probability mass function of Xk xk -1 1 2 P(XK=xk) 1/6 1/2 1/3 Where…

Q: Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: The probabilities of a random variable X are given as when x, =, Plz) =} 1 2 -1 1 P(x,) = 2 and X2…

A:

Q: Show that there are no values of c such that f(x) = cx can serve as the values of the probability…

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Q: random variable

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Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0≤x≤ 1. Find…

A: Given that X follows U(0,1) E(x) =1/2 V(x) =1/12   Y|X=x follows N(x, x) Here, we consider mean…

Q: Suppose X, Y are two discrete random variables with probability function given by: Y\X -1 1 1/8 1/8…

A:

Q: If the discrete random variable X has the pmf for 2-1,0,1,3, a = find E(X), and var(X).

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

Q: Verify central limit theorem for the independent random variablesX,, where for each k, P{X =± 1} = .

A:

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

A:

Q: Let x1, x2X. be a random sample of size (n) taken from Poisson( 8), and y = 2x, then F(x1, x2 , X,…

A: Poisson Distribution: A discrete random variable X is said to follow Poisson distribution with…

Q: The Poisson random variable X, has pmf f(2)- A, for z = 0, 1,2,3,.... Which of the following is…

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Q: Suppose that W is a discrete random variable which takes on values: 12, 17, 22, 27, 32, 37, 42, 47,…

A:

Q: Let X1 and X2 be continuous random variables with the joint probability - function fx1,x,(x1, x2),…

A: Hello! As you have posted 2 different questions, we are answering the first question (2.2.5). In…

Q: Let random variables X1 and X2 have the ioint pdf as

A: From the given information, fx1,x2=e-x1+x2, x1>0, x2>0 Consider,…

Q: Suppose that X₁, X₂, X3 are mutually independent random variables with the respective generating…

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

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)30.5, P(2)=0.2 and…

A: The discrete random variable X takes only three values 0, 2, and 3. The probabilities are P0=0.5,…

Q: Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2)…

A: Result: if X~χ2(n) Mx(t)=(1-2t)-n/2 If X and Y are independent then E(XY)=E(X)E(Y)

Q: Let X and X1, X2, ... be random variables. Then |Xn – X| 1+|X, – X| X, 4 X as n →∞ → E 0 as n → 0.

A: Solution: From the given information, X and X1, X2 …be random variables.

Q: Suppose X is a discrete random variable with moment generating function 1 2 1 3t 4t Mx(t) + 3 + 12

A: Answer - X is discrete random variable with moment generating function                 Mx(t)  = 14…

Q: Suppose X is a discrete random variable with pmf defined as p(x) = log10 fo x = {1,2,3,...9} Prove…

A: A pmf is legitimate if (i) 0≤P(x) ≤1                                   (ii) ∑P(x) =1

Q: (4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).

A:

Q: Letx X2,bp å dzntically distributed random variables with finite second moment Show that nP [Ix) 7…

A: The answer is given using the concept of normal distribution.

Q: 4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?

A: It is given that E(X) = μ and Var(X) = σ2