Let X be Bernoulli random variable, find the moment generating function X and find its mean, variance and third moment.

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: IEX is a Poisson distribution variable, then its moment generating function is e^(e' -1).

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Q: Suppose that the number of customers that enter a bank in an hour is a Poisson random variable, and…

A: Given,A random variable X~Poisson(λ)P(X=x)=e-λλxx! ; x≥0and  P(X=0)=0.09

Q: the moment generating function of the random variable is always exist

A: The moment generating function of a random variable x, Mx(t) always exists. or not?

Q: A synoptic uses Bernoulli random variable X to describe the weather conditions within one year…

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Q: Let Y be a discrete random variable with probability mass function (pmf), p (y). The mean of Y can…

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Q: Let the random variable X assume the value r, with probability law P(X=r) =q P, Find the moment…

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Q: Decide whether the random variable x is discrete or continuous. x represents the length of time it…

A: We know that discrete variables take a finite number of countable points whereas a continuous random…

Q: Let X be a random variable for a discrete uniform distribution. If −1≤X≤5−1≤X≤5, what is the…

A: Answer:- Let X be a random variable for a discrete uniform distribution. If −1≤X≤5 what is the…

Q: let X denote a random variable that has a Poisson distribution with mean y = 3 find p(x≥4/x≥2)

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Q: Use the uniqueness of moment-generating functions to give the distribution and the mean of a random…

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Q: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 find the mean and variance of…

A: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 We need to find the mean and…

Q: Find the expected value and variance of the a geometric random variable X with parameter p using its…

A: The expected value and variance of the a geometric random variable X with parameter p using its…

Q: let X be a random variable and X is normally distributed

A: Given information:  μ=35 and σ=4

Q: Let X be a random variable that follows the Poisson distribution with a mean of Find: a. Р(X-0) b.…

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Q: The characteristic function for a Gaussian random variable X, having a mean value of zero, is ¢, (@)…

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Q: Find the moment-generating function ?(?) for a Poisson distributed random variable with mean ?.

A: Solution-: We want to find moment-generating function  for a Poisson distributed random variable…

Q: Suppose that X is a Poisson random variable with X 5. Approximate the probability that 7 < X < 10

A: 4) Given, Suppose that X is a Poisson random variable with λ=5. Poisson distribution: PX=x=e-λλxx!…

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: let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

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Q: Exercise 7: Let the random variable X have a discrete uniform distribution on the integers 0≤x≤99.…

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Q: . Derive the moment generating function of Bernoulli(p). Calculate the mean and the variance of the…

A: We have given that  The random variable X follows Bernoulli (p). Here, we need to find the mgf of…

Q: Let X1, X2, X3... X20 be a random sample from a distribution with mean 8 and variance 5. Find the…

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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 zand y be two independent Gaussian random variables, both with expected value zero and variance…

A: Given, x and y be two independent gaussian random variables.    We have to find the power spectral…

Q: Let X and Ybe independent standard Normal random variables. Find the joint distribution of X2 +Y2…

A: From the given information, X and Y are independent standard normal random variables. Given that…

Q: The probability distribution of the discrete random variable X is   Find the mean and variance of…

A: There is slightly mistake in the probability distribution.  It should be, P(X=x) = 3x14x343-x Which…

Q: A portfolio has 100 independent insurance policies. Each policy has a probability 0.8 of making no…

A: X 10 50 80 P(X) 0.4 0.4 0.2

Q: Let X denote a random variable that has a Poisson distribution with mean 1= 2. Find (a) P(X = 4) %3D…

A: Here X~ Poisson with parameter 2. We need to find the required probabilities.

Q: a. Find the moment-generating function of Y = X₁ + X₂ + ... + X₁. b. What is the distribution of the…

A: Given : X1,X2.....Xr be independent exponential random variables with parameter λ we have to find…

Q: Suppose that the number of customers that enter a bank in an hour is a Poisson random variable, and…

A: Given,P(X=0)=0.05A random variable X~Poisson(λ)P(X=x)=e-λλxx!  ;   x≥0

Q: The following table gives the joint probability distribution of two random variables X and Y. Find…

A: Provided table gives the joint probability distribution of two random variables X and Y .  Formula…

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

A: let the probabilty function is ,f(x)=Cx4      x&gt;1             0         otherwise

Q: Let x be a Poisson random variable with μ = 0.9. Find the probabilities for x using Table 2. (Round…

A: Let X follows Poisson distribution with mean 0.9

Q: Let X be Poisson random variable with the mean λ. Find the value of λ that satisfies P(X = 0|X ≤ 2)…

A: Let X be a random variable which follows Poisson distribution with a population mean λ. X~P(λ) The…

Q: What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?

A: The parameter of the Poisson random variable is l.

Q: Let ã be a random variable with an invertible cdf F. What is the distribution of Fa(ã)? Justify your…

A: a~ is Random Variable with invertible cdf Fa~. Therefore, P(a~ ≤ t) = Fa~(t) Let, Fa~-1 be the…

Q: Let Z be the standard normal random variable Find P (Z > -0.72)

A: Given that  X~N(0,1) be a standard normal distribution To find P(Z&gt;-0.72)=?…

Q: Let X be a discrete random variable with expectation -0.5 and variance 3. Let Y=−2X+8, find the…

A: The expectation and variance of discrete random variable X are -0.5 and 3, respectively.

Q: Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4

A: We have given that the characteristics function of random variable X and we have to calculate the…

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: Let X1 and X2 be independent standard normal random variables. Show that the joint distribution of

A: Given information: It is given that X1 and X2 are independent standard normal random variables.

Q: Find the expected value and variance of F

A: Given :  (i) The expected value and variance of  (ii)

Q: Let X be a random variable that follows the Poisson distribution with a mean of 6. Find: a. РX-0) b.…

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Q: Let X1, X2, X3… X20 be a random sample from a distribution with mean 8 and variance 5. Find the mean…

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Q: Suppose that the number of customers entering a bank in one hour is a Poisson random variable and…

A: We have given that  P(X=0)=0.02 We use poisson probability distribution.  I want to find mean and…

Q: Let X be a discrete random variable with PGF P(s) = a. Find the probability distribution of X. b.…

A: * SOLUTION :-    From the given information the answer is provided as follows

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.