GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 64 of 65

Marks: +1, -0

{X}

is random variable with uniform probability density function in the interval

[-2,10]

. For

Y=2 X-6

, the conditional probability

P(Y ≤ 7 ∣ X ≥ 5)

(rounded off to three decimal places) is

. . . . .

Solution:

Given

(0.3

0.3)

f_{x}(x)=\{\table 1 {/} 12 , -2 ≤ x ≤ 10 ; 0 , \;\text " otherwise "\;.

y=2 x-6

So,

f_{y}(y)=\{\table 1 {/} 24 , -10 ≤ x ≤ 14 ; 0 , \;\text " otherwise "\;.

x ≥ 5

then

y ≥ 4

So,

P(y ≤ 7 {/} x ≥ 5)=P(Y ≤ 7 {/} y ≥ 4)

=\;{P(4 ≤ y ≤ 7)}/{P(4 ≤ y ≤ 14)}=\;{3}/{10}=0.3

Go to Question:

Prev Question

Next Question