Show that, if X and Y are independent random variables, such that E\X| < 0,and B is an arbitrary set, then EXI{Y E B) = EX P(Y E B).

Q: A class contains 50 students. The probability of failing in one of the courses for each : 0.035, but…

A: From the given information, There are 50 students. The probability of failing in one of the courses…

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: Consider a discrete random variable X with a pmf given by i) ii) iv) p(x) = cx2, if x = 1,2,3,4 0,…

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Q: E\VX{ + X}

A: Consider the provided question, Let X1,X2 be the two independent standard normal random variables.…

Q: Exercise 3. Let X be a random variable with mean µ and variance o². For a E R, consider the…

A: Farmula used  V(X)=E(X2)-[E(X)]2

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t)…

A: Here Coin Is tossed 3 times So Here We can use Binomial Distribution with n=3,p=0.5 Now For number…

Q: Show that the mean and variance of the random variable Y are 0 and 1, respectively.

A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1,

Q: Suppose X and Y are jointly discrete random variables, the conditional expectation of u(x), given…

A: X and Y are discrete random variables. Need to obtain: The conditional expectation of ux

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: Tay-Sachs disease is a rare fatal genetic disease occurring chiefly in children, especially of…

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Q: The CDF of a random variable X is given the function F(x)= Cx² 3x² + x support of X is x=1,2,3,....…

A: Given that, the CDF of a random variable X is given the function                      F(x)=cx23x2+x…

Q: Let Y₁ 1 X=(x,-X₂), where X, and X₂ are independent random variables and each of them is distributed…

A: Given that the independent random variables X1 and X2 follows χ22 distribution.

Q: A class contains 50 students. The probability of failing in one of the courses for each student is…

A: From the given information, There are 50 students. The probability of failing in one of the courses…

Q: Find k if the joint probability distribution of X, Y, andZ is given by f(x, y, z) = kxyzfor x = 1,…

A: The joint probability density function is given as f(x,y,z)=kxyz For x=1,2 ;y=1,2,3 ,z=1,2. Compute…

Q: et X1, X2, ... , Xn form a random sample from U(0,0). Find al sufficient statistics.

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Q: 2. Let X,Y: → R be simple random variables. Show that X+Y and XY are also simple random variables.

A: Random Variable :- A random variable is a function from sample space Ω  into the real numbers. To be…

Q: Exercise 3. Let X be a random variable with mean and variance o2. For a € R, consider the…

A: Let X be the  random variable with mean μ and variance σ2. For aεℝ i.e. E(X)=μ and V(X)=σ2 We know…

Q: Let X ∼ N (0, 1) and Y ∼ Ber(p) be two independent random variables. find the law of S = X + Y

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Q: Suppose a and b be two possible values of a random variable X with a > b. The probability that X…

A: Explanation: Cumulative distribution function CDF  gives the area under the curve and represented by…

Q: Let E₁, E₂F, with E₁ E₂ = 0). Define X = IE₁ + IE₂. (a) Show that X is a random variable. (b)…

A: The objective of the question is to prove that X is a random variable and to calculate the standard…