Question

If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.

Options

• `16/15`

• `15/16`

• `31/16`

• None of these

Answer 1

If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to none of these.

Explanation:

We have, f(x) = `k/2^x`, x = 0, 1, 2, 3, 4

Since, f(x) is a probability distribution of a random variable X, therefore we have

`sum_(x = 0)^4 f(x)` = 1

`\implies sum_(x = 0)^4 (k/2^x)` = 1

`\implies k sum_(x = 0)^4 1/2^x` = 1

`\implies k(1 + 1/2 + 1/2^2 + 1/2^3 + 1/2^4)` = 1

`\implies k((16 + 8 + 4 + 2 + 1)/2)` = 1

`\implies k xx (31/16)` = 1

∴ k = `16/31`