Let X be a binomial np random variable What are the values o

Let X be a binomial n,p random variable. What are the values of the following probabilities? Explain why. (a) P(X greater than or equal to 0) (b) P(X less than or equal to n) (c) P(X=2.5) (d) P(x = n+1)

Solution

in binomial n represents the total number of trials and x represents the total number of successes

(a) P(X greater than or equal to 0)

      = 1- p(x<0) = 1-0 =1

reason : number of successive trials cannot be less than zero

(b) P(X less than or equal to n)

= 1- p(x>n) = 1-0 =1

reason : number of seccessive trials will never exeed the number of total trials

(c) P(X=2.5)

not defined (Impossible)

reason : number of successive trials cannot be fractional value. is, it should be an intiger.

(d) P(x = n+1) = 0

number of seccessive trials will never exeed the number of total trials