A random variable X has the following probability distribution:
Determine:
i. The value of a
ii. P (X<3), P (X≥3), P(0<X<5).
The key point to solve the problem:
If a probability distribution is given then as per its definition, Sum of probabilities associated with each value of a random variable of given distribution is equal to 1
i.e. ∑(pi) = 1
∴ Sum of probabilities = 1
∴ a+3a+5a+7a+9a+11a+13a+15a+17a = 1
a(1+3+5+7+9+11+13+15+17) = 1
Thus, a = ………..ans (i)
P(X<3) = P(X = 0) + P(X = 1) + P(X = 2)
= a+3a+5a
= 9a =
P(X≥3) = 1 - P(X<3) {∵ sum of probabilities in distribution is 1}
=
P(0<X<5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= 3a + 5a + 7a + 9a
= 24a
= ……..ans (ii)