Consider 4 trials, each having the same probability of success. Let X denote the total number of successes in these trials.

If E[X]=0.8, find each of the following.

(a) The largest possible value of P{X=4}

(b) The smallest possible value of P{X=4}.

In this case, give possible values for the remaining probabilities:

P{X=0};

P{X=1};

P{X=2};

P{X=3};

a) 0.2

b) 0

Step-by-step explanation:

E[X] = 0*P (X=0) + 1*P (X=1) + 2*P (X=2) + 3*P (X=3) + 4*P (X=4) = 0.8

(a) The largest possible value of P (X=4) occurs when

P (X=1) = P (X=2) = P (X=3) = 0.

In that case,

4*P (X=4) = 0.8 = ==> P (X=4) = 0.8/4 = 0.2

(b) The smallest possible value of P (X=4).

Obviously, the smallest possible value is P (X=4) = 0

In that case, possible values for the remaining probabilities

could be, for example

P (X=0) = P (X=2) = P (X=3) = 0

P (X=1) = 0.8