Question

discrete probability distribution: basic
fill in the ( p(x = x) ) values to give a legitimate probability distribution for the discrete random variable ( x ), whose possible values are ( -6, -3, 2, 3 ), and ( 6 ).

value ( x ) of ( x ) ( p(x = x) )
( -6 ) ( 0.12 )
( -3 )
( 2 ) ( 0.28 )
( 3 )
( 6 ) ( 0.17 )

Explanation:

Step1: Recall the property of probability distribution

For a discrete probability distribution, \(\sum_{x}P(X = x)=1\). Let \(P(X=-3)=a\) and \(P(X = 3)=b\). Then \(0.12+a + 0.28+b+0.17=1\).

Step2: Simplify the equation

Combine the known values: \(a + b=1-(0.12 + 0.28+0.17)=1 - 0.57=0.43\).
Assume \(a=b\) (since no other constraints are given for \(P(X=-3)\) and \(P(X = 3)\) in the problem statement). Then \(a=b=\frac{0.43}{2}=0.215\).

Answer:

\(P(X=-3)=0.215\) and \(P(X = 3)=0.215\)