If X is uniform random variable on interval (2,7) then the expexted value of X equal 9/2 (1/2 (5/2

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: A single observation of a random variable having a hypergeometric distribution with N = 7 and n = 2…

A: Hyper geometric distribution: In a population with N objects, M be the number of success event. A…

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

Q: Let X be a nonnegative random variable. Prove that. EX (EX) 4E[X*] 2

A: Given that X be a nonnegative random variable. Result: PX≥c≤E(X2)c2               ≥c2EX2

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 discrete random variable with range Rx = {0, ), such that Px(0) = Px() = Px() = Px() =…

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Q: The pdf of a uniform random variable is given by: Ax) = 7aSxs a and r>6

A: Task: From the given information, f(X)=2x, 0≤x≤1 Here, the given density function is continuous…

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: Show that for ν2 > 2 the mean of the F distributionis ν2ν2 − 2 , making use of the definition of…

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Q: Suppose the manufacturer of an item wants to test Ho p= 0.8 against H1 p= 05 for a binomial random…

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Q: Let X, be independent Bernoullli random variables with the probability of success, Σχ f(x,e) =…

A: Solution

Q: Which of the following is equal to Cov (X+ Y, 2X +Y), where X and Y S ? are random variables on a…

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Q: Let X be a random variable representing a risk with E(X) = 10 and E(X) = 125. %3D A portfolio…

A: Given  E(X)=10, E(X2)=125, n=25  Note this Probability value calculated from standard normal…

Q: Suppose that Y Еxponential() ~ and let X = exp{-Y/ß} be a new continuous random variable. If…

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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: Suppose that the random variable X has the following df. F(x) = {0 for x≤0, 1-ex for x>0 Determine…

A: The given dF is : F(x)=0for x≤01-exfor x>0 We want to find quantile function.

Q: Two random variables X and Y have joint char- acteristic function yl@,m)=exp(-2@,² – 80;) (i) Show…

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Q: 4. For two independent random variables such that X sin N(0, 4), Y ~ U[0, 4], Var(2X +3Y) = Var(2X -…

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Q: Let X1,..., be a sequence of random variables with 1 P(X, = +) = 1 P(X, = 0) = 1 - n2 %3D 2n2 (a)…

A: Given: P(Xn=0)=1-1n2 P(Xn=±1)=12n2 (a) Mean of Xn.…

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: 2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. d.…

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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: Suppose you have two random variables X,Y ux,Hy,o o3,0xY where Cov(X, Y) = 0x.Y You sample both…

A: The provided information is: n=81x¯=50y¯=55σ2x=25σ2y=144σxy=34.50

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

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Q: Let X1,..., X, be independent U (0, ve) random variables for some 0 <0< 1. Find an MLE of 0.

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Q: X1 and X2 are independent random variables each distributed as N (0, 1). Show that the MGF of (X,-…

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Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

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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 is a discrete random variable. Let the pmf of X be equal to f(x) = 5 – x /10 , x = 1,2,3,4…

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Q: Let X, be independent Bernoullli random variables with the probability of success, f(x,e) = e*(1-…

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Q: Suppose you have a random sample X1. X2,.X, where: • X = 1 if a randomly selected student uses a car…

A: Given information: Given that the ransom sample X1, X2, … , Xn are binomial random variables.

Q: If the random variable X is uniformly distributed over I V3 сотрute V3 30 and compare it with the…

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Q: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

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Q: X and Y are independent random variables uniformly distributed over (0, 1). Compute the probability…

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Q: Let Y1, Y2, ..., Y, denote iid uniform random variables on the interval (0, 5X). Obtain a method of…

A: we want to find the estimator of lambda by using method of moment and MLE  given  y1=2.5, y2=1.5,…

Q: 2. Suppose that a random variable X has a discrete distri- bution with the following p.f.: cx for x…

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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,…

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Q: let X(n,p) denotes binomial random variable with parameters n and p. Show that X(n+1,p) >st (…

A: Given Information: X(n, p) denotes binomial random variable with parameters n and p where n is the…

Q: (a) A stick of length 1 meter is broken into two pieces at a randomly chosen point on the stick.…

A: (a) When we break the stick into two pieces at a point x, we will be left with one piece of length x…

Q: Find the first two moments about the mean for the random variable X defined by X =-2 with prob. 1/3…

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Q: If X is a continuous random variable with distribution, f(x) =*+ k if 0 < x< 3 = 0 elsewhere…

A: if X is a continuous random variable with distribution,f(x)=x6+kif 0≤x≤30elesewhere

Q: Suppose that the time. in days, required to repair a heat pump is a random variable X having a gamma…

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Q: (2) Suppose that for all n > 1, the nth moment of a random variable X is (n+3)!3"-1 Find the…

A: Given that,           For all n≥1, the nth moments of a random variable X is…

Q: Let X1, X2, ..., Xn be independent and identically distributed random variables, X ∼ Exp(λ). Show…

A: Given  X1, X2, ..., Xn be independent and identically distributed random variables X ∼ Exp(λ) The…

Q: 2.) The 'r'th cumulant of the sum of independent random variables is equal to the sum of the 'r'th…

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

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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: For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???

A: Given - Cov ( X , Y ) = -0.9 Z = 3-X

Q: Suppose a random variable Y uniformly distributed over the interval [2, 7]. 1. What is f(y)?

A: It is given that Y follows Uniform(a = 2, b = 7) To find : The probability density function of Y.

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!