x is a uniform random variable in the interval (x1,x2). Find the expected value of x

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A: Moment generating function:

Q: The probability distribution of the discrete random variable X is: f(X) = k2³-x , for x = 4,5, 6, 7…

A: Hello! As you have posted 2 different questions, we are answering the first question 1  with 3…

Q: Let X₁, X₂ and X3 be mutually independent random variables with Poisson distributions having means…

A: X~Pois(λ) P(X=x)=e-λ λx/x! x=0,1,2,3,..,..

Q: x is a uniform random variable in the interval (x,, x,). Find the expected value of x.

A: ANSWER: For the given data,

Q: Let the random variable X assume the value r, with probability law P(X=r) =q P, Find the moment…

A:

Q: The continuous random variable X has a cumulative distribution function F(x) given by: x 2. Find…

A: The CDF of X is given by, Fx = 0x<1kx4+x2-21≤x≤21x>2 Now, X is continuous random variable. So,…

Q: x <0 F (x) = 3x 0 < x <1 2 1

A: Let X be the continuous random variable having cumulative distribution function F(x)

Q: Let X be the random variable with the cumulative probability distribution: 0 F(x)= 1 = {xx ²₁ x 2…

A:

Q: Let X be a random variable representing a risk with E(X) = 10 and E(X2) = 125. %3D A portfolio…

A:

Q: Exercise 23. Let X be a random variable having the uniform distribution on the interval (0,0+ 1), 0…

A:

Q: Let X be a random variable with distribution function F(x) = 1-e*,x > 0, then the p.d.f of X is

A: Here given cumulative distribution function of x

Q: Let the random variable X fit uniformly in the interval (-1,1). Find the distribution of the random…

A: Given: The random variable X follows a uniform distribution in the interval (-1,1). Let Y=X2…

Q: Let the random variable X have the moment generating function e³t M(t) = 1-t²-1<t<1 What are the…

A:

Q: Let X be the random variable with the cumulative probability distribution: 0 x < 0 J F(x) = {kx² 0…

A:

Q: The distribution function for a random variable X is (1- e-2x x 2 0 F(x) %3D x < 0

A: From the given information, F(x)=1-e-2x, x≥00              x&lt;0 a) Density function: f(x)=ddxF(x)…

Q: 3. Find the maximum likelihood estimator of 0> 0, using the random sample {X1,. , Xn}, whose…

A: # Given CDF of random variable x is  F(x)=1-e^-(x^2/2*theta)   : x&gt;0  then to find maximum…

Q: For a continuous random variable X. we can compute the probability of P (a < X<b) by O Fibl-Fla) O…

A: GivenP(a&lt;X≤b)

Q: X and Y be two discrete random variables with a joint p en by X-0 X-2 Y=1 0.03 0.02

A: to find P(X&gt;0 and Y≤3)

Q: 1. Find the value of c to make f (x) = x = 2, 3, 4 into a valid probability distribution. Enter…

A: Given, f(x)=cx2x-1                   x=2,3,4

Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

Q: Let X ~ U(a,b). Use the definition of the mean of a continuous random variable to show that μX =…

A: The mean of the uniform continuous random variable can be calculated as:

Q: Find the Mean of f(x), where f(x) = 6X+6. The probability distribution of a random variable X ; if X…

A: Mean is an average value around which the whole data set is concentrated.…

Q: Suppose the discrete random variable X has probability function 1. px(1) I = 1,2, 3, I(I +1)"

A: Given  :    pxx  =1xx+1,  x=1,2,3,...

Q: X is a discrete random variable with p.m.f given by P(X=x)= x/c where c is a constant. The support…

A:

Q: Let Z and Y be discrete random variables taking values 0 with the corresponding distributionms P(Z =…

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

Q: Let Xo, X1, X2, ... be independent random variables such that X, has an exponential distribution…

A:

Q: what is E[XY]?

A:

Q: The probability mass function of a random variable X is given by f(x) = cx2 for x = 3,4,5. Compute…

A: 4) Given that the probability mass function of a random variable X is, f(x)=cx2,x=3,4,5 Consider,…

Q: The discrete random variable X has the probability function, where k is canstant kx x=2,4,6,8, 10 f…

A:

Q: Let X1, ... , X49 be a random sample of 49 independent and identically distributed uniform…

A: Given that X1,X2,....X49 be a random sample of 49 independent and identically distributed uniform…

Q: Let the probability function of the random variable X be defined as f(x)=cx^4 for x > 1, otherwise…

A: let the probabilty function is ,f(x)=Cx4      x&gt;1             0         otherwise

Q: x < 0 0 < x < 2 2 F (x) = 3x 8 2 1 2 < x

A: The cumulative distribution function of the continuous random variable X is given by F(x)  is a…

Q: Derive the expected value of Y? Suppose that a random variable Y is uniformly distributed on an…

A:

Q: b) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {kx²…

A:

Q: Let X be the random variable with the cumulative probability distribution: x < 0 F(x)=kx², 0 < x < 2…

A:

Q: Find the distribution of Z X+Y, if X and Y are jointly continuous random variables F given by

A: Given information: The joint probability density function of the random variables X and Y is given.

Q: Let be a continuous random variable whose cdf is F(x ). Then P(X=0)=.... ... .A .B 1 .C F(x) .D…

A:

Q: Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e-²x;…

A:

Q: Let Y - Bernoulli(X) where X is a random “probability of success" parameter. Let X Uniform(0, 1).…

A: Step 1  Given that : Y follows bernoalli(x)  distribution with parameter x. And x follows uniform (…

Q: Assume that X and Y are independent continuous random variable: distributed on the interval [1,12]…

A:

Q: Q1: Let X1, X2~iid U(0,1), find the probability that the random interval 3X2' X2 includes . 3

A:

Q: Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e -²x…

A:

Q: The continuous random variable X is uniformly distributed over the interval [2.5, 3.5|].

A:

Q: Let the probability function of the random variable X be defined as f (x) = cx² for 0≤x≤1, otherwise…

A: Let X is the random variable: fXx=cx20≤x≤10otherwise a). The value of constant c: ∫-∞∞fXudu=1 So:…

Q: a) Find the value of the constant c

A: The joint pdf is given by f(x,y) = c(2x+y)

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. Find…

A: Given: X follows a  normal distribution with mean -1 i.e. µ= -1 and the standard deviation of 1 i.e.…

Q: Let X1, X2, X3, X4 be independent random variables of size 4 from a gamma distribution - xª-1e G(a,…

A: We want to find E(Z)=?  Where Z=X1+X2

Q: A continuous random variable X has cumulative distribution function F(x) = 1.5 3 2 6 –1 < x < 1. a)…

A: (a) To evaluate the expectation by definition, we need to derive probability density function first,