Answer to Question #84704 in Statistics and Probability for Lim Yi Chen

Question

The number of cars seen in the car wash in any given hour is a random variable represented
by X. The probability distribution for X is:
X 5 6 7 8 9
P(X) 0.3 0.2 m 0.2 0.1
Stated that, the probability of 7 cars arriving in any given hour is three times higher than the
probability of 9 cars arriving.
Based on the information given, find m. Comment on your finding.

Answer 1

Since it is stated that "the probability of 7 cars arriving [that is

$$m$$

] in any given hour is three times higher than the

probability of 9 cars arriving [which is

$$0.1$$

]", we can calculate that

$$m=3P(X=9)=3\cdot 0.1=0.3.$$

However in this case the sum

$$\Sigma P(X)=0.3+0.2+0.3+0.2+0.1=1.1>1,$$

which means that this is not a valid probability distribution.