Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

Q: Let X be a discrete random variable with PMF Px(X) = { (0.5, x=2) (0.3, x=5) (0.2, x=6) (0,…

A: Let X be a discrete random variable with PMF Px(X) , and CDF F(X), the CDF is defined as F(X) = P(X…

Q: The probability distribution of X is given as: f(x) = { 0.4; x = 1 (x-1)/4; 1 < x < 2 (3-x)/4; 2…

A:

Q: The expected value and variance of the random variable X are as follows:         E(x) = 716.04…

A: Given data is E(x)=716.04Var(x)=48656.04given linear equation is…

Q: f(x, y) y 1 3 1 0.05 0.05 0.00 2 0.05 0.10 03 3 0.10 0.35 0.10

A: The table is as follows       x     f(x,y)   1 2 3 h(y)   1 0.05 0.05 0.1 0.2 y 3 0.05 0.1…

Q: (i) Find the mean of X (ii) Find the variance of X

A: Given,(i)we calculate the mean of let's calculate the mean:Here we have findoutThe

Q: (a) A lower bound for P(6<Y <24) (b) the value of k such that P(|Y-15| ≥k) ≤ 0.09.

A:

Q: No, this solution is not correct. The variance of an exponentially distributed random variable is…

A: We are given that L is exponentially distributed with a mean of 1/Y, where Y has a gamma…

Q: Can you please help me calculate the expected value of x and the variance of x.

A: x p(x) x*p(x) x2*p(x) 0 0.0278 0 0 1 0.0833 0.0833 0.0833 2 0.1389 0.2778 0.5556 3 0.1944…

Q: Given f(x) = { (x2+1)/30; x = -2,-1,0,1,2  0; elsewhere ] Find the mean and variance of X.

A: X-2-1012f(x)

Q: p. Let Z Let X, Y be independent geometrically distributed random variables with parameter = E[X|X +…

A: Given:X, Y are independent geometrically distributed random variables with parameter p.The expected…

Q: Calculate the expected value E(X) for the given random variable X. Select 13 cards without…

A: From the provided information, Total cards in standard deck = 52 13 cards selected without…

Q: Y is a random variable and "a" and "b" two real constants. Without resorting to the properties of…

A: Given that, Y is a random variable and "a" and "b" two real constants. Without resorting to the…

Q: E(X2) is greater or equal to [ E(X)2] . Hint: Recall the definition of variance.

A: E(X) implies mean of X and E(X2) implies mean of X2. Variance measures how far a set of number is…

Q: Let X and Y be independent random variables such that E(X)=2, E(Y)=2, var(X)=2, and var(Y)=2…

A: We know that, If X and Y are independent random variables.  Var(X+Y)= Var(X)+ Var(Y)

Q: What is the formula for the variance? o S? =E (x - X)? / n o S? = E (X - x)? /n o S2 = E (x - X) / n…

A: Variance is one of the measures of dispersion.

Q: -75 degrees Fahrenheit. It has recently...) a Gaussian random variable T with mean u = – been…

A: T is a Gaussian random variable. Mean (μ)=-75 P(T&lt;-80)=0.1587 The objective is to find the…

Q: Let y be a normally-distributed random variable with mean u= 100 and variance 2 = 16: Select which…

A: We know If random variable X ~ N(a, b2) where mean(x) = a, standard deviation(x) = b.  then,  P(a-b…

Q: Let X be a discrete random variable that is the value shown on a single roll of a fair die. (a) What…

A: Step 1: Step 2:  Step 3: Step 4:

Q: Let T be a random variable. If E(T) = a+b0, find an unbiased estimator of 0. Is the mean- squared…

A: