Practicing Success
A random variable X has the following probability distribution
Then value of P for $(0 < X < 5)$ |
\(\frac{1}{5}\) \(\frac{2}{5}\) \(\frac{4}{5}\) \(\frac{3}{5}\) |
\(\frac{4}{5}\) |
P(X) = 1 ∴ P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) = 1 ∴ 0 + k + 2k + 2k + 3k + k2 + 2k2 + 7k2 + k = 1 9k + 10k2 - 1 = 0 10k2 + 9k - 1 = 0 ⇒ 10k2 + 10k - k - 1 = 0 10k (k + 1) - 1(k + 1) = 0 ⇒ (k + 1)(10k - 1) = 0 ∴ k +1 = 0 k = -1 k ≠ -1 ∴ 10k - 1 = 0 $k = \frac{1}{10}$ ...(i) Value of P(0 < x < 5) = 0 + k + 2k + 2k + 3k $8k = 8×\frac{1}{10}=\frac{8}{10}=\frac{4}{5}$ Option 3 is correct. |