Question

A man with 5 keys wants to open his door and tries the keys at random. Exactly one key will open the door. Determine the probability distribution of random variable X if X is the number of trials required to open the door. Assume that unsuccessful keys are NOT eliminated from future trial.

Answer 1

Answer:

Step-by-step explanation:

Given that a man with 5 keys wants to open his door and tries the keys at random.

Exactly one key will open the door.

Assume that unsuccessful keys are NOT eliminated from future trial.

So the probability of choosing correct key = 0.2 = constant since unsuccessful key is not eliminated

X = no of trials required to open the door

We find that X is discrete taking values 1,2....infinity because there is a chance that continuously unsuccessful keys are drawn

P(X=x) = Prob that x-1 trials are unsuccessful and xth trial is successful

=$0.8^{x-1} (0.2)$, x=1,2.....

is the pdf of X

This is a Geometric distirbution.