Question

A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P (X = 3) = 2 P (X = 1) and P (X = 2) = 0.3, then P (X = 0) is

विकल्प

• 0.1

• 0.2

• 0.3

•  0.4

   

Answer 1

 0.4

Let:
P(X = 0) = m
P(X = 1) = k.

Now,
P(X = 3) = 2k
 

xi	pi	pixi
0	m	0
1	k	k
2	0.3	0.6
3	2k	6k

 

Mean = \[\sum\nolimits_{}^{}\] p_ix_i

\[0 + k + 0 . 6 + 6k = 1 . 3\]
\[ \Rightarrow 7k = 1 . 3 - 0 . 6\]
\[ \Rightarrow k = \frac{0 . 7}{7} = 0 . 1\]

We know that the sum of probabilities in a probability distribution is always 1.

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

\[\Rightarrow m + 0 . 1 + 0 . 3 + 0 . 2 = 1\]
\[ \Rightarrow m + 0 . 6 = 1\]
\[ \Rightarrow m = 0 . 4\]