Question

Fill in the P(X = x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 2, 3, 4, 5, and 6. Value I of x P(x = x) 2 0.16 3 4 0.17 0.29 6 0 X 6 For Subm

Answer 1

Dear student, we can solve one question at a time, please help to upload other questions separately. Here, I am answering question 2.

X	P(X)	X**2	(X**2)*P
1	0.25	1	0.25
2	0.05	4	0.2
3	0.15	9	1.35
4	0.15	16	2.4
5	0.1	25	2.5
6	0.3	36	10.8
		Sum	17.5

Expected E(X) = ΣX*P(X) = 1*0.25 + 2*0.05 + 3*0.15 + 4*0.15 + 5*0.1 + 6*0.3 = 3.7

E(X) = 3.7

Var(X) = Σx²p − μ²

^{Var(X) = 17.5 - 3.7**2 = 17.5 - 13.69 = 3.81}

^{Var(X) = 3.81}