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Let X(n, p) denote a binomial random variable with parameters n and p. If P1 P2, show that X(n, p) st X(n, p2)

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See the attached question.

Introduction to binomial distribution:Consider a random experiment involving n independent trials, such that the outcome of each trial can be classified as either a &ldquo;success&rdquo; or a &ldquo;failure&rdquo;. The numerical value &ldquo;1&rdquo; is assigned to each success and &ldquo;0&rdquo; is assigned to each failure.Moreover, the probability of getting a success in each trial, p, remains a constant for all the n trials. Denote the probability of failure as q. As success and failure are mutually exclusive, q = 1 &ndash; p.Let the random variable X denote the number of successes obtained from the n trials. Thus, X can take any of the values 0,1,2,&hellip;,n.Then, the probability distribution of X is a Binomial distribution with parameters (n, p) and the probability mass function (pmf) of X, that is, of a Binomial random variable, is given as:

Given information:Here, it is given that X(n,p) is a binomial random variable with parameters n and p.Consider a binomial random variable X1= X(n,p1).Consider another binomial random variable X2= X(n,p2).If X(n,p) is a binomial random variable, then the mean and variance for the binomial variate X are E(x) = n * p and V(x) = n *p *(1 &ndash; p).Since, X1 is a binomial random variable with parameters n and p1, the mean of the binomial random variable X1 is E(X1) = np1.Since, X2 is a binomial random variable with parameters n and p2, the mean of the binomial random variable X2 is E(X2) = np2.

Calculation to show that X(n,p1) ≥st X(n,p2):From the below given calculation, it is proved that X(n,p1) ≥st X(n,p2):...

Let X(n, p) denote a binomial random variable with parameters n and p. If P1 P2, show that X(n, p) st X(n, p2)

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Let X(n, p) denote a binomial random variable with parameters n and p. If P1 P2, show that X(n, p) st X(n, p2)

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