Suppose a and b are positive integers with a ≤ b. Let random variable X take on the value of a power of 2 in the range [2^a , 2^b ] where each power of 2 has equal probability. Find E[X]

Q: Use secant method to determine a root of f(x) = x 4 - x – 10 with initial guesses of x-1 = 1 and xo…

A: Secant Method:- Let a function f(x) then the roots of function f(x) is  xn+1=xn-fxnxn-xn-1fxn-fxn-1;…

Q: se R’s “pbinom()” function to verify Chebyshev’s inequality for k=2 and k=3 when X follows…

A: Given that, X follows Binomial distribution with parameters n=30 and p=0.2. Mean of Binomial…

Q: Without using R or any technology, for what value x does P(X<x) = 0.5? How do you know?

A: Let X ~ N(150, 12) μ=150 σ=12 The standard normal variate is defined as: Z=X-μσ~N(0,1)

Q: There is an average of four accidents per month at an intersection. Assume that a month has 30 days.…

A: The variable X is defined as the number of accidents. There is an average of four accidents per…

Q: Suppose X ~ Bernoulli(0.5), Y ~ Bernoulli(0.1), independent. What is Var(X*Y)?

A: We have given that  X ~ Bernoulli(0.5), Y ~ Bernoulli(0.1)The variance of Bernoulli distribution  is…

Q: Kim throws a ball against a wall at time t = 0 At time t = 1 , it hits the wall and then at time t =…

A:

Q: Let the pdf of X be f(x)=3x^2,  0<x<1. Find the probability that X is greater than 0.3.

A:

Q: Find the first 5 terms of {b_n}={n/e^n}.

A: In a sequence, each element is called as a term. For finding the terms of a sequence, we need to put…

Q: Graph the function f(x)=-5x^2-6  On [0,4] And find the average value over the interval

A: We have to find average value

Q: Suppose that Var(X) = 879.05, Var(Y) = 8681.72, and Cov(X,Y) = 2281.58. What is Var(.08X + .92Y)?

A: The objective of the question is to find the variance of the linear combination of two random…

Q: Evaluate f,5 28 - 7 a3 +4 a2 dz. Round your answer to two decimal places. s1, 5 28 – 7 23 + 4 a2 da=…

A: Given: ∫-115x8-7x3+4x2 dx

Q: - Exercise 5.- Calculate the mean value of the function f(x) = 2(x − 1)³ - 5(x-1)² +6 in the…

A: Mean Value Theorem for Integrals: If is continuous on the closed interval and differentiable on…

Q: Find a number that c satisfied the conclusion of the mean value therorem for f(x)=x^3 +x -1 on the…

A: According to question given that f(x)=x3+x-1,   interval 0,2

Q: Suppose that Var(X) = 704.85, Var(Y) = 9161.83, and Cov(X,Y) = 2154.62. What is Var(.97X + .03Y)?

A: