Let (X_1, ..., X_k) be a multinomial distribution with probabilities p_1, ..., p_k in n independent...

Let (X_1, ..., X_k) be a multinomial distribution with probabilities p_1, ..., p_k in n independent trials. Calculate E(X_i), and COV(X_i, X_j) for 1 <= i, j <= k.

Expert Solution

milcah answered 1 year ago

Define multinomial distribution for X ,Y,Z with an example and MGF of multinomial distribution and also...

Define multinomial distribution for X ,Y,Z with an example and MGF of multinomial distribution and also give mean, variances of X,Y,Z.

Define multinomial distribution for X ,Y,Z with an example. MGF of multinomial distribution and give mean,...

Define multinomial distribution for X ,Y,Z with an example. MGF of multinomial distribution and give mean, variances of X,Y,Z.

In a binomial distribution n = 10 and p = 0.30. Find the probabilities of the...

In a binomial distribution n = 10 and p = 0.30. Find the probabilities of the following events: (Round the final answers to 3 decimal places.) a. x = 2. Probability b. x ≤ 2 (the probability that x is equal to or less than 2). Probability c. x ≥ 3 (the probability that x is equal to or greater than 3). Probability

In a binomial distribution, n = 8 and π=0.33 . Find the probabilities of the following...

In a binomial distribution, n = 8 and π=0.33 . Find the probabilities of the following events. Use Appendix B.1. (Round your answers to 4 decimal places.) x=2 . x≤2 . x≥3 . x=2 x≤2 x≥3.

In the binomial probability distribution, let the number of trials be n = 4, and let...

In the binomial probability distribution, let the number of trials be n = 4, and let the probability of success be p = 0.3310. Use a calculator to compute the following. (a) The probability of three successes. (Round your answer to three decimal places.) (b) The probability of four successes. (Round your answer to three decimal places.) (c) The probability of three or four successes. (Round your answer to three decimal places.)

1. Let ?1, . . . ?? be ? independent random variables with normal distribution of...

1. Let ?1, . . . ?? be ? independent random variables with normal distribution of expectation 0 and variance ? 2 . Let ?̂︁2 1 be the sample variance ??, ?̂︁2 2 be 1 ? ∑︀ ? ?2 ? . (1) Show that the expectation of ?̂︁2 1 and ?̂︁2 2 are both ? 2 . In other words, both are unbiased point estimates of ? 2 . (2) Write down the p.d.f. of ?̂︁2 1 and ?̂︁2 2....

Let Y have the lognormal distribution with mean 78.8 and variance 160.20. Compute the following probabilities....

Let Y have the lognormal distribution with mean 78.8 and variance 160.20. Compute the following probabilities. (You may find it useful to reference the z table. Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answers to 4 decimal places.) P(Y > 106) P(74 < y < 106)

In a sequence of independent flips of a fair coin, let N denote the number of...

In a sequence of independent flips of a fair coin, let N denote the number of flips until there is a run of three consecutive heads. Find P(N ≤ 8). (Should write out transition matrix.)

Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution...

Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution formula

Let N1 , N2 , N3 follow a trinomial distribution with parameters n, assume that n...

Let N1 , N2 , N3 follow a trinomial distribution with parameters n, assume that n follows a Poisson distribution with parameter λ > 0. Also assume that, conditionally on N, the random variables N1, N2, N3 follow a trinomial distribution with N trials and category probabilities p1, p2, p3 with p1 + p2 + p3 = 1. Compute the covariance and correlation of (N1,N2)

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