- Akia selects at random a value from the continuous random variable \(W\), which is uniformly distributed over the interval \([ a , b ]\)
The probability that Akia selects a value greater than 17 is \(\frac { 1 } { 5 }\)
The probability that Akia selects a value less than \(k\) is \(\frac { 53 } { 60 }\)
- Find the probability that Akia selects a value between 17 and \(k\)
It is known that \(\operatorname { Var } ( W ) = 75\)
- Find the value of \(a\) and the value of \(b\)
- Find the value of \(k\)
- Find \(\mathrm { P } ( - 5 < W < 5 )\)
- Find \(\mathrm { E } \left( W ^ { 2 } \right)\)