4 Let X be a discrete random variable with PGF P,(s) = () %3D 3 Find the probability distribution of X. Derive the mean and variance of X using its PGF. a. b.

Q: Let X be a normally distributed random variable with mean 600 and variance 10,000. Find two values A…

A: Given Information Mean µ = 600 Variance V(x) = 10000 Standard deviation is given by

Q: Find the mean and variance of the uniform probability distribution given by f(x)=1/n for x=1,2,3,4……

A: Given pdf is: f(x)=1n    for x=1,2,3,4.....

Q: Let X be a discrete random variable with the following probability distribution -3 6 P(X=x) Find…

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Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

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

Q: Let X be a random variable with a mean equal to 100 and a standard deviation equal to 15. Let…

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Q: Find the distribution function of the random variablethat has the probability distribution f(x) =…

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Q: Suppose X takes the value 1 with probability P, and the value 0 with probability (1-P). The…

A: Variance formula is:

Q: A random variable Z is normally distributed with mean and variance are 0 and 1 respectively.…

A: Given Mean=0 Standard deviations=1

Q: Q/ The probability distribution of random variable X is: 3. P(x) 0.1 0.3 0.5 0.1 iTY-X+2X Find: 1.…

A: Given Y= X2+2X So we find Y for every X X 0 1 2 3 Y 0 3 8 15 P(Y) 0.1 0.3 0.5 0.1

Q: An irregular die with six faces produces scores, X , for which the probability distribution is given…

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Q: Consider the experiment of rolling 2 dice and define Y to be the A.V. that record the sum of the…

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Q: because all airline passengers do not show up their reserved seat, an airline sells n = 125 tickets…

A: Let X be the random variable representing the number of passengers, out of 125, showing up to board…

Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

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

Q: Let x be a dis crete random variable with probability distribution fCx) =k (x² + 20) and x =…

A: i. From the given information, the probability distribution function is f(x) = K (X2 + 20) and x=…

Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k

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Q: Let the random variable X fit the binomial distribution with parameters (p,N). Find the variance by…

A: Solution : Given : X ~B(p, N) where, p = probability of success N= no. of trials x = no. of…

Q: Let the random variable X fit the binomial distribution with p=1/2 , n=3 parameters. Plot the…

A: Given Data: n=3 p=0.5   Distribution function is also known as cumulative function

Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

A: Hypothesis testing is conducted for the parameters of the population like population mean,…

Q: Answer must be a fraction in lowest term. * The probability distribution of the discrete random…

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Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: A random variable Z is normally distributed with mean and variance are 0 and 1 respectively.…

A: Solution

Q: X is a discrete random variable such that the possible values are {a, a+1, a+2, ... b-1, b}. The…

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Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

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Q: Find the approximate mean and variance of Y = √X, where X is a random variable following a Poisson…

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Q: The probability distribution of the discrete random variable X is 3-x x = 0,1,2,3. .4, Find the…

A: Solution-: We have the p.m.f. of X is given by,  f(x)=3x*(14)x*(34)3-x f  ;  x=0,1,2,3;   We find…

Q: Find the mean the of the probability distribution of the random variable if P(X) = x-3/15 for X= 7,8…

A: Formula : μ = E(x) = Σx * p(x)

Q: A random variable Z is normally distributed with mean and variance are 0 and 1 respectively.…

A: Given that the mean is 0 and the variance is 1. Z~Nμ=0,σ=1 We will use the standard normal…

Q: The random variable Z has the probability distribution shown below If  E(Z) =4 2/3find the values…

A: Given Information: The probability distribution of the random variable Z is given as: z 2 3 5 7…

Q: A random variable Z is normally distributed with mean and variance are 0 and 1 respectively.…

A:

Q: Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater…

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Q: probability distribution and has a mean value of 25 and a variance of 9. Calculate: i. P(X > 26)…

A: Given that  Mean = M =  25 , Variance = V = 9 , Standard deviation = SD = 3

Q: Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the…

A: Given data: Mean = 6 Variance = 4 Thus, Std. Dev = sqrt(variance) = sqrt(4) = 2

Q: Let the random variable x have a normal distribution with a mean value of 70 and a variance of 25.…

A: Given data: Mean = 70 Variance = 25 To find: P (x < 80 ) = ?