Probability distribution calculator
Give the values of a random variable X and their probabilities - with an unknown like k if the question has one - and get k, the mean, the variance and the standard deviation with the working table ISC Mathematics expects.
Answer
- k
- 1/10
- Mean E(X)
- 2
- E(X²)
- 5
- Variance
- 1
- Standard deviation
- 1
Finding k
- The probabilities add up to 1: k + 2k + 3k + 4k = 1
- So k = 1/10.
Working
| x | P(x) | value | x·P(x) | x²·P(x) | F(x) = P(X ≤ x) |
|---|---|---|---|---|---|
| 0 | k | 1/10 | 0 | 0 | 1/10 |
| 1 | 2k | 1/5 | 1/5 | 1/5 | 3/10 |
| 2 | 3k | 3/10 | 3/5 | 6/5 | 3/5 |
| 3 | 4k | 2/5 | 6/5 | 18/5 | 1 |
- Mean = Σ x·P(x) = 2
- Variance = Σ x²·P(x) - (mean)² = 5 - (2)² = 1
- Standard deviation = √variance = 1
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