Find the value of K such that the following are the probability distributions: (a) P(X) = K/X³ where X 1, 2, 3,4 (b) P(X) = KX? where X = 0.5, 0.25, 0.75 Also Compute the Mean and Variance of the above distributions.

Q: (a) Find the expectation E (X) of X. E (x) = [ (b) Find the variance Var(X) of X. Var (x) = 0

A: Consider , the table , x P(x) x*P(x) x^2*P(x) 0 0.4 0 0 1 0.05 0.05 0.05 2 0.15 0.3 0.6 3…

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: C. Find the mean of X of the probability distribution of the discrete random variable X. 3-x 3 f(x)…

A: Given that ; A discrete  probability mass function (pmf) is given here.  By comparing the pmf  of…

Q: The probability function of the random variable X is defined as f(x)=cx²(1-x)² for 0<x<1, otherwise…

A: Given information: The probability distribution function of the random variable X is defined as:…

Q: The probability mass function of a discrete random variable is: 37-x A G for x = 1, 2, ., 14 (a)…

A: Solution-: We have, P(X)=a*(15)x(32)7-x   for x=1,2,3,.........14 We compute (a) P(3&lt;X≤9)=? (b)…

Q: The discrete random variable X has probability mass function kx x 2,3 x+1' 2kx P(X =x) = x=4,5 x-1'…

A:

Q: (a) Find the expectation E (X) of X. E (X) = [] (b) Find the variance Var(X) of X. Varlx) = D

A: The following table shows the provided outputs of the discrete random variables, along with the…

Q: (8) Find the variance of X when X is distributed as N(0, 1). The correct answer is -1 1 -2 N/A…

A: Given that that X~N(0,1).

Q: The probability mass function of a discrete random variable is: 7-x p(x) = a(=) G) for x = 1,2, .,…

A: Solution-: We have the p.m.f. of a discrete random variable P(X=x)=a*(15)x*(32)7-x   for…

Q: 2n- 50 and p= 0.45

A: Given, Let, n =number of trials p =the probability of success q=1-p

Q: 1. Let the random variable X be the time in seconds between incoming telephone calls at a busy…

A:

Q: The Joint probability distribution of X and Y is given below: Y 0.4 0.1 1. 0.2 0.3 Find the…

A:

Q: The cumulative probability distribution for the random variable X 0, x<0 F(x)= 8 3x2 Osx<2 given as.…

A:

Q: a) Suppose that random variables X₁ and X₂ have exponential distribution with expected value of and…

A: It is given that X1 ~ Exponential(1/2) And X2 follows Exponential(1/3)

Q: Let the joint probability distribution function of two random variables X and Y be given by f(x, y)…

A:

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

A: Solution: From the given information, the probability function of X is

Q: Determine the value k so that the given function can serve as a probability distribution of the…

A:

Q: A random variable X has a normal distribution with mean 250 and variance of 625. If x = 300, then…

A: Given mean=250, variance=625 we have to find Z value

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: 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: 4. The continuous random variable X is defined as following, X-Unif(-2, 0.5). a. Graph the pdf of X.…

A: According to guidelines we solve three subparts

Q: 4. The continuous random variable X is defined as following, X-Unif(-2, 0.5). a. Graph the pdf of X.…

A: Given : The continuous random variable X is defined as following, X ~ Unif(-2, 0.5).

Q: 1. The random variable Y = X2 does not have a normal distribution because the probability density…

A: The p.d.f of normal distribution is given by,

Q: A batch contains 35 bacteria cells and 14 of the cells are not capable of cellular replication.…

A: Given: There are total 35 bacterial cells out of which 14 bacterial cells are not capable of…

Q: Let X be a random variable that assumes values-1 and 1 with probability 2/3 and 1/3 respectively. If…

A: The probability function of X is given by X -1 1 P(x) 2/3 1/3

Q: y -2 1 4 -1 0.2 0.1 0.2 3 0.1 0.2 0.1 0.1

A: We need to find P(X=5)

Q: Find the mean and the variance of the uniform probability distribution given by f ( x ) = for x = 1,…

A:

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

A:

Q: Q3/ Let the random variable X has a poisson distribution with mean u. find the d.f. of Y = c,X + C2…

A:

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

A: The probability mass function of a random variable is defined on the range of the random variable,…

Q: The discrete random variable X has the probability distribution given by: -3 1 3 7 P(X = x) 2r 0.25…

A:

Q: 13. A discrete random variable has probability function f (x) = 1/ 2* where x = 1, 2, . . .. Find…

A: A discrete random variable has probability function p(x). Then, a. Mode is that value of x where…

Q: Q1: If the random variable (x) has a uniform distribution on the interval [0,6]. Find: a) P(1 < x<…

A: The probability density function of uniform distribution is given below: fx=1b-a, a≤x≤b0,…

Q: The probability mass function of a discrete random variable is: 7-x p(x) = a=) G) for x = 1,2,., 14…

A:

Q: If the random variable X is exponentially distributed with parameter λ = 4, then the probability P(X…

A: Given: λ=4 X ~ Exp (4) P(X ≤ 0.25) needs to be calculated

Q: 3) Find the mean and variance of the random variable X with probability function or density f(x).…

A: NOTE :  As per Bartleby instruction when more then one question is given only one has to be…

Q: If the probability density function of the random variable X p(1-p)*-1 if x =1,2,3,..,. otherwise…

A: Probability Density Function: It is a statistical function, describing all the possible outcomes of…

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

A:

Q: The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has…

A:

Q: Let X be a random variable with expected value E(X) = 1 and variance Var(X) = 4. Find E(3X +2) and…

A: From the provided information, E (X) = 1 and Var (X) = 4

Q: Let X1,.., Xn, be a random sample from the following probability distribution x+1 fX(x)=0De-*/", x >…

A: Solution:  a)  fX(x)  = x+1θ(θ+1) e-xθ             : x &gt;0 and θ&gt; 0 Joint pdf is given by,…

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: The is a function given by the probability that the random variable X is less than or equal to x,…

A: We have to determine the function which gives probability that X is less than or equal to x.

Q: Suppose the random variable X has the following probability density function f (2) = 2 %3D otherwise…

A: The given probability density function is, fx=x2      0≤x≤20        otherwise

Q: A random variable X has the following distribution function: x <0 0.1x 0<r<3

A: Given information, FXx=0   x&lt;00.1x    0≤x&lt;30.4x-0.6     3≤x&lt;41                x≥4

Q: If the probability density function of random variable X is given by: = {k(x-1)(2-x), 0, 15xS 2;…

A:

Q: A continuous random variable x is normally distributed with a mean of 1 and a standard deviation of…

A: Given Mean μ=1, standard deviations σ=0.2  X~N(μ=1, σ=0.2) P(X=0.5)=?

Q: 5. If the probability density function of a continuous random variable X is Sca" 0<x < 1 cx' f (x)…

A: