7) Allow a continuous probability distribution to be defined as f(x) = x/2 for the range 0 sxs2. %3D Demonstrate that the area underneath the curve is 1 (the function integrates to 1) and calculate the mean and variance of the probability distribution.

Q: Let X be a random variable with pdf f(x) = kx*,-1 <x< 1. Find E (X).

A:

Q: A random variable x follows continuous uniform distribution on the interval [18,38]. Find the…

A:

Q: Let m(t) =(1/6)e^t+(2/6)e^2t+(3/6)e^3t Find E(y) Find V(y) Find the distribution of y

A:

Q: egral for a probability is diver

A: Integral for a probability is divergent: The probability of X landing somewhere between a and b is…

Q: Let X a b(4,) find Var(3x) and distribution function.

A:

Q: The average value of the residuals is

A: Residual is the error happen in the observation. It is calculated by subtracting the observed and…

Q: Assume that x has a normal distribution with mean =4 and standard deviation q=2. Find (3<x<6)

A: Given   x has a normal distribution  mean μ=4  standard deviation σ=2 Find p(3&lt;x&lt;6)=?

Q: Spray drift is a constant for pesticide applications and agricultural producers. Suppose that the…

A:

Q: X1,..., X, are independent, identically distributed RVs with mean u and variance g2. Find the mean…

A:

Q: The heights (x) of students are normally distributed with mean 152 cm and standard deviation 30 cm,…

A: normal distribution μ = 152 cmσ = 30 cmP(x&lt;140) = ?

Q: Let X be the lifetime (measured in hours) of an electronic device. suppose that X let X be a…

A:

Q: The amount of water in a reservoir at the beginning of the day is a random variable X and the amount…

A: The amount of water left in the reservoir at the end of the day: Z= X-Y

Q: Let X ~ I(2,8). Find the distribution of Y = 2x.

A:

Q: Today, the waves are crashing onto the beach every 5 seconds. The times from when a person arrives…

A: Given,A random variable X~U(0,5)f(x)=15    ;  0≤X≤5

Q: Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y =…

A: X~ Uniform (-2,2)  Then we have to find pdf of Y=X5

Q: The concentration by volume  of methane is at a point on center line of jet of natural gas mixing…

A: It is given that concentration by volume  of methane is at a point on center line of jet of natural…

Q: Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Assume that X donotos the continuous random varlable with probability distribution of y & (A) and…

A: Basic probability

Q: Find the characteristic function of X² when X has the N(u, o²) distribution.

A:

Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,