(2) Let X be a random variable with p.d.f (3x² +6x) [>x>0 S(x) =- , then p(x < 1) is O.W (a) 1 (b) 2 (c) 3 (d) 4 (e) None of these

Q: Calculate E((X +Y)²).

A:

Q: (1) Let X be a random variable with p.d.f. ke 2x f(x) ={ 0 <x<0 , then o.w (a) k=3 (b) k=2 (c) k =-…

A: Reviewing information, X is a r.v. with pdf, f(x)=k·e-2x                                   ;…

Q: 2. Let X₁, X₂₁.... X ₁ be a i.i.de Sequence of random variables. Show that Cov (X₂X₁ X) = 0₁ V₂ =…

A:

Q: 3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2)…

A: X and Y are independent U(0,1) random variables:Objective: Show that:

Q: c) Suppose that X and Y are jointly continuous random variable - x f(x,y) = {o* for 0< x <1 and 1< y…

A:

Q: (3) Let X be a random variable with p.df 12(3x+ 0<x<1 15 , then P(0<x< 0.5) is o.w 7 (d) 7 (a) 60…

A:

Q: 1-4x 10) If a random variable assumes 4 values with probability 1+3x 1-x 1+2x and ¹-4 4 4 4 the…

A: Here for given probability check whether using value of x total probability is equal to 1 and all…

Q: (1) Let X be a random variable with a function x= 0,1, 2,3 4 xt(3-x)! S(x)=- , then E(x+1) is o.w…

A:

Q: (b) Let X~N(40,144) and if Y = 2X - 1 Find the following probabilities: (i) P(X 50) (iii)P(35 < X S…

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

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

A: Discrete random variable is defined as a variable which can take only specific values. For example…

Q: (1) Let X be a random variable with a function (3 4 x! (3-x)! S(x) =- x= 0,1, 2,3 . then E(x+1)is…

A:

Q: 6x) 0<x<1 S(x)%=D , then p(x<1) is (a) 1 (b) 2 (c) 3 (d) 4 (c) None of these

A: It is an important part of statistics. It is widely used.

Q: (1) Let X be a random variable with a function [3 1 x= 0,1,2,3 4 x! (3-x)! fx) = { , then E(x) is…

A: Given, X is a random variable with the function below

Q: (1) Let X be a random variable with a function (3 1 4 xt (3-x)! *- 0,1, 2,3 , then E(x+1) is o.w (e)…

A:

Q: Suppose that X is a random variable * ? having the following p.d.f. , Find Var(x) { 2(1 – x) 0 < x <…

A: Given: f(x)=2(1-x) , 0&lt;x&lt;1 The formula to compute the mean is: V(x)=∫x2fx dx-∫xfx dx2

Q: Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)?…

A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

Q: -. Determine the constant c so that f(x)=cx, x=1, 2, 3,...,10 satisfies the conditions of being a p.…

A: The given probability distribution can be desctibed as X 1 2 3 4 5 6 7 8 9 10 f(x) c 2c 3c 4c…

Q: If x is a random variable such that x-b(1,2) then P(V ( x) <x<E (x ) )is? X

A:

Q: If random variable X is such that E[(X-1)]=10, E[(X-2)] = 6, what is σ'

A:

Q: 10- If the random variable X has the gamma p. d. f with integer parameter a and arbitrary ß> 0, then…

A:

Q: (36) Let X be a random variable with p.d.f. xe2k x=1,2,3 f(x)= , find (1) k (2) E(x²) O.w

A: Given : Let X be a random variable with pdf :              f(x) = xe2k              ; x = 1,2,3…

Q: (34) Let X be a random variable with p.d.f. x= 1,2,3 f(x) ={ , find (1) k (2) E(²) O.w

A: X is a random variable with pdf: The sum is always 1. So,

Q: Let X be a random variable defined by 0. 2. 3 4 P(X = x) k 2k 2k 2k 2k Then E(X) and V(X) are equal…

A:

Q: Which of the following is equal to Cov (X + Y, 2X – Y), where X and Y are random variables on a…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!