Suppose (S, P) is a binomial distribution with n trials and probability of success p. Let X be the random variable X(k) = k³, where k is the number of successes. Calculate E[X].

Q: There are thirty Exam P takers at a certain testing center. The probability of failing the exam is…

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Q: Determine the value of c such that f(x) = (c / x2) for x > 1 represents the p.d.f. of a random…

A: Given that  f(x)=c/x2   , x>1

Q: X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 1/4…

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Q: Calculate the expected value E(X) of the given random variable X. X is the number of tails that come…

A: Given Information: No. of times a coin is tossed/No. of trials (n)=58 P(tail in a coin)=0.5

Q: The probability distribution of X is given as: f(x) = { 0.4; x = 1 (x-1)/4; 1 < x < 2 (3-x)/4; 2…

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Q: The velocity of a particle in a gas is a random variable X with probability distribution fx(x) =…

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Q: A random variable X has the following pdf: f(x) = 9xe-3"; x > 0

A: Given: random variable x with gamma distribution with pdf  f(x)=9*x *e^-(3x)  : x&gt;0  then to find…

Q: X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20,…

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Q: Let X, and X, be independent exponential distributions with the same parameter 1. What is the joint…

A: Given:  X1 &amp; X2 are independent random variables with pdfs             f(x1)=λe-λx1; x1&gt;0…

Q: Let X denote the number of VCRs sold during a random week by a certain store. The probability…

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Q: Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

A: Given that X follows Uniform (a,b)  We have to find E(X) , Variance and E(X2)-E(X)

Q: et X be a discrete random variable with P(X = -2) = .1, P(X = 1) = .15, P(X = 2) = .4, P(X = 4) =…

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Q: Let x be a Poisson random variable with mean = 6. Find the probabilities for x using the Poisson…

A: The variable x be a Poisson random variable with mean .

Q: Determine the expected value and standard deviation of a random variable Y=2X+100 when X has a pmf…

A: Solution: The probability mass function of random variable X is  x 2 3 4 5 Total  f(x)  0.3 0.3…

Q: Prove that the E(X) = 1/p for a geometric distribution, where x is the number of trials.

A: The geometric distribution with probability that ranges from 0 to 1 is a discrete probability on the…

Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

A: Given that  Let X and Y be random variables having the same distribution.If X and Y are independent,…

Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: Let Z be a discrete random variable taking one of the four distributions, Bernoulli, Binomial ,…

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