Chapter: Probability Distributions· Mathematics & Statistics (Commerce) Part 2
The probability distribution of \(X\) is as follows :\(x\)01234\(P(X = x)\)0.1\(k\)\(2k\)\(2k\)\(k\)Find : (a) \(k\) (b) \(P(X \lt 2)\) (c) \(P(1 \le X \lt 4)\) (d) \(F(2)\)Solution : The table gives a probability distribution.\(\therefore \Sigma p_i…
Q.6 (C)(ii) The probability distribution of \(X\) is as follows :
| \(x\) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \(P(X = x)\) | 0.1 | \(k\) | \(2k\) | \(2k\) | \(k\) |
Find : (a) \(k\) (b) \(P(X \lt 2)\) (c) \(P(1 \le X \lt 4)\) (d) \(F(2)\)
Solution : The table gives a probability distribution.
\(\therefore \Sigma p_i = 1\)
\(\therefore 0.1 + k + 2k + 2k + k = 1\)
(a) \(k = \square\)
(b) \(P(X \lt 2) = P(X = 0) + P(X = 1) = \square\)
(c) \(P(1 \le X \lt 4) = P(1) + P(2) + P(3) = \square\)
(d) \(F(2) = P(X \le 2) = P(0) + P(1) + P(2) = \square\)