Question

A random variable has the probability distribution table as shown. Calculate P(X≤1).

x -3 | -2 | -1 | 0 | 1

P (X = x) | - | - | 0.3 | 0.1 | 0.1

Answer 1

The given probability distribution table is:

x	-3	-2	-1	0	1
P(X = x)	-	-	0.3	0.1	0.1

Let ‘b’ be the missing values. So,

x	-3	-2	-1	0	1
P(X = x)	b	b	0.3	0.1	0.1

Assume P( X = -3 ) = P(X = -2) = b.

It is known that the total sum of all the probabilities equals 1, so find the missing value ‘b' as shown below,

P( X = -3 ) + P(X = -2) + P( X = -1) + P(X = 0) + P(X = 1) = 1

b + b + 0.3 + 0.1 + 0.1 = 1

2b + 0.5 = 1

2b = 1 – 0.5

2b = 0.5

b = 0.5/2

b = 0.25

Thus, the complete probability distribution table is,

x	-3	-2	-1	0	1
P(X = x)	0.25	0.25	0.3	0.1	0.1

Now, calculate as shown below,

Therefore, the required value is 1.