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2). Let X(n, p) denote a binomial random variable with parameters n andp. Show that X (n 1,p) st X (n, p)


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2). Let X(n, p) denote a binomial random variable with parameters n and
p. Show that X (n 1,p) st X (n, p)

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2). Let X(n, p) denote a binomial random variable with parameters n and p. Show that X (n 1,p) st X (n, p)

Step 1

Given X(n,p) is a binomial random variable with parameters n,p.
n is total number of trails
p is probability of success.
The probability distribution function of binomial distribution for k number of success with parameters n,p is shown below

Р(х: п,р) -
(п-х)!! Р * (1— р)"

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n! Р(х: п,р) - (п-х)!! Р * (1— р)"

Step 2

Any binomial random variable with low p and low n values distribution is left tail, for large p and small n values, distribution is right tail and for large n and for p = 0.5 the distr...

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