A random variable X is binomial10075 A random variable Y is

A random variable X is binomial(10,0.75) A random variable Y is created by the transformation Y = g(X), where g(x) = {0 x

Solution

x is binomial with (10,0.75)

Mean Y = 4.680

var Y = 23.314-4.68^2 =1,414

Mean of x = 7.5

x	0	1	2	3	4	5	6	7	8	9	10
p(x)	0.0000009	0.000286	0.00039	0.0031	0.0162	0.0584	...
Y	0	1	2	3	4	5
p(y)	0.0000009	0.000286	0.00039	0.0031	0.0162	0.9210
xp	0	0.000286	0.00078	0.0093	0.0648	4.605
x^2p	0	0.000286	0.00156	0.0279	02592	23.025