Probability Distribution/ Solving Random Variables

Question

1.    An experiment was conducted where rats have injected virus and check if they will survive or not. Find the probability that at most 2 rats will survive given the probability distribution of the random variable X that measures the number of surviving rats.

X	0	1	2	3
P(X)	0.21	0.44	0.29	0.06

Answer 1

This is a discreet probability distribution, where the probabilities for each distinct value of the random variable (X) is specified. We need to create an equation that specifies "at most 2 rats" which would survive translates to measuring the probability that 2 or 1 or 0 rats survived.

Converting to an equation then , P ( X < 2) = P (X = 2) + P (X = 1) + P (X = 0)

= 0.29 + 0.44 + 0.21

= .94

There is 94% probability that at most 2 rats will survive.

Alternatively, this can be solved by using the complement.

P ( x < 2) = 1 - P (X > 2)

= 1 - P (X = 3)

= 1 - .06

= .94

This last method comes in very handy when you have a large number of X values in the distribution.