Question

In: Statistics and Probability

Suppose X ∼ U(0, 12). (a) Find the mean and standard deviation for X. (b) Find...

Suppose X ∼ U(0, 12).

(a) Find the mean and standard deviation for X.

(b) Find P(x > 7).

(c) Find P(x > 5 | x < 10).

Expert Solution

X~ U( 0,12)

f(x) = ; 0<x < 12

= 0; otherwise

a) Mean , E(X) = =

Standard deviation = = = 3.4641

b) P( X>7) =

=

= [12-7]

= 5/12

c) P( X>5 | X < 10) =

So first, P( 5<X < 10) =

=

= [10-5]

= 5 / 12

Now, P( X <10) =

=

= [10-0]

= 10/12

P( X>5 | X < 10) = = = 5/10 = 0.5

orchestra answered 2 years ago

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