Question

II. 1. The range of a random variable X is {0,1,2). Given that
P(X = 0) = 3c", P(X = 1)=4c-10c2, P(X = 2)=5c-1
(i) Find the value of c (ii) P(X<I), P(1<x2) and (P(0<X53)​

Answer 1

Answer:

The range of a random variable X is {0,1,2}.

Given that P(X=0)=3C

3

,P(X=1)=4C−10C

2

,P(X=2)=5C−1. Find the value of:

(i) C

(ii) P(X<1)

(iii) P(1<X≤2) and P(0<X≤3).

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Video Explanation

Solution To Question ID 609962

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Answer

(i) We must have ∑P(X)=1

⇒P(X=0)+P(X=1)+P(X=2)=1

⇒(3C

3

)+(4C−10C

2

)+(5C−1)=1

⇒3C

3

−10C

2

+9C−2=0

⇒(C−1)(3C

2

−7C+2)=0

⇒(C−1)(C−2)(3C−1)=0

⇒C=1,2,

3

1

Also 0≤P(X=0),P(X=1),P(X=2)≤1

So only acceptable value of C is

3

1

(ii) P(X<1)=P(X=0)=3(

3

1

)

3

=

9

1

(iii) P(1<X≤2)=P(X=2)=4C−10C

2

=4⋅

3

1

−10⋅

9

1

=

9

2

and

P(0<X≤3)=1−P(X=0)=1−

9

1

=

9

8

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