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005_5d9r8jk-aflscbfb.doc
Answered Same Day Dec 23, 2021

Solution

David answered on Dec 23 2021
130 Votes
Answer 1.
The number of black balls = m
The number of white balls = n
Student A picks a ball from the bag.
Probability that the ball drawn by A is black =


Without return, the Student B picks a ball.
Probability that the second ball drawn by B is black :
There are two cases.
1. If the ball drawn by A is black.
Probability that the 2nd ball picked by B is black =


( )
2. If the ball drawn by A is white.
Probability that the 2nd ball picked by B is black =


( )
Answer 2.
Given : X is uniformly distributed over [-п/2 , п/2]
Y = sinX
To determine : f(y)
Solution :
It is given that X is uniformly distributed over [-п/2 , п/2].
This implies that the probability fX(x) is constant in [-п/2 , п/2].
Let fX(x) be some constant k.
As we know; ∫ ( )


For the given domain; ∫ ( )



As fX(x) = k
∫



k∫



k (x) = 1
k (


(

))
k ( )
k = 1/
thus;
fX(x) = 1/
P(a < X < b) = ∫ ( )



= ∫



= ∫



= k (b - a)
= (b - a)
now; Y = sinX = g(x)
fY(y) = fY (g(x))
= fX (g
-1 (y) )
= fX (sin
-1 (Y) )
= sin-1 (Y)
Points plotted :
Y...
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