Question

Prof. Alil lways finishes his lectures within 2 min after the official cdass end tme. Let X be a RV denotes the time that elapses between the official 0 otherwise Find the probability that Prof. Ali finishes his dlass within 1 he finishes his class within 1 min only one time. min? And,if Prof. Alil has 4 lectures this month, find the probability that within this month O 0.125 and 0.335 0.037 and 0.1323 0 0016 and 0.0596 O 0.008 and 0.03124

Answer 1

The probability that prof. Ali finishes his class within 1 min is

$P(X\leq 1)=\int_{0}^{1}f(x)dx=\int_{0}^{1}\frac{3}{8}x^{2}dx=\left [ \frac{x^{3}}{8} \right ]_{0}^{1}=\frac{1}{8}=0.125$

----------------

To find the answer of second question question we need to use binomial disrtibution with parameters n=4 and p=0.125. So the required probability is

$P(Y=1)=\binom{4}{1}(0.125)^{1}(1-0.125)^{4-1}\approx 0.335$

First option is correct.