The random variable \(X\) has a continuous uniform distribution over the interval \([ - 3 , k ]\) Given that \(\mathrm { P } ( - 4 < X < 2 ) = \frac { 1 } { 3 }\)
find the value of \(k\)
A computer generates a random number, \(Y\), where
\(\quad Y\) has a continuous uniform distribution over the interval \([ a , b ]\)
\(\mathrm { E } ( Y ) = 6\)
\(\operatorname { Var } ( Y ) = 192\)
The computer generates 5 random numbers.
Calculate the probability that at least 2 of the 5 numbers generated are greater than 7.5