A dart is thrown at a dashboard with radius of 7 cm. The point that the darrt hits is uniformly distributed on the circular dashboard. Find the expected distance of that point from the center of the dashboard.

Let R = radius

P(R > r ) = P(X^2 + Y^2 > r^2)

=

=1-[(r^2)/49]

E[R] = int[ P(R > r ) ]

= 14/3

My question is: how did he get

Let R = radius

P(R > r ) = P(X^2 + Y^2 > r^2)

=

**[ 49(pi) - (pi)r^2 ] / 49(pi)**=1-[(r^2)/49]

E[R] = int[ P(R > r ) ]

= 14/3

My question is: how did he get

**[ 49(pi) - (pi)r^2 ] / 49(pi)**
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