Density and Median

[Yankel]

Help please

The diameter of a ball is a random variable X with the next density:

2x if 0<x<=0.5
1 if 0.5<x<=1
f(X)= 0.25 if 1<x<=2
0 else

a. What is the diameter of balls that half of the diamteres will be smaller than him (median) ?

b. What is the probability that among 50 balls (chosen randomly), at least 30 balls will have a diameter of more than 0.5 ?

 

[amul28]

u have that
f(x)=2x if 0<x<=0.5
=1 if 0.5<x<=1
= 0.25 if 1<x<=2
=0 else

now
(a)let X be the diameter
P((X/2)<0.5)=P(X<1)

(b)P(at least 30 balls will have a diameter of more than 0.5 )
P(X>30) given that diameter is more than 0.5 select
f(x)=1
so P(X>30)=integration over({0.5 to 2})(1) dx

NOTE: Im not sure about part-(a)...

 

[Dason]

Part a is just asking for the median correct? Just figure out what the CDF (call it F(x)) and then find when F(x) = .5