x is a random variable with the probability function: f(X) = x/6
for x = 1, 2 or 3 the expected value of X is?
2.333
1/6, 1/3, 1/2
Find out
Well, well, well. Looks like we're dealing with some probabilities here. Let's calculate the expected value step by step:
To find the expected value, we need to multiply each value of the random variable by its corresponding probability and then add them all up. So let's do some math, shall we?
E(X) = (1 * f(1)) + (2 * f(2)) + (3 * f(3))
Plug in the probability function:
E(X) = (1 * 1/6) + (2 * 2/6) + (3 * 3/6)
Simplify:
E(X) = 1/6 + 4/6 + 9/6
Now, let's add those fractions up, shall we?
E(X) = 14/6
Simplify some more:
E(X) = 7/3
So, my friend, the expected value of X for x = 1, 2, or 3 is 7/3. And there you have it, a beautifully calculated expected value!
To find the expected value of a random variable, you need to multiply each possible value of the random variable by its corresponding probability, and then sum up those products.
In this case, the random variable X can take on the values 1, 2, or 3. The probability function for X is given as f(X) = x/6.
To find the expected value, E(X), we need to calculate:
E(X) = (1/6) * 1 + (2/6) * 2 + (3/6) * 3
Let's break down the calculation step by step:
Probability of X = 1: f(1) = 1/6
So, the product is (1/6) * 1 = 1/6.
Probability of X = 2: f(2) = 2/6
So, the product is (2/6) * 2 = 4/6.
Probability of X = 3: f(3) = 3/6
So, the product is (3/6) * 3 = 9/6.
Now add up the products:
E(X) = 1/6 + 4/6 + 9/6 = 14/6 = 7/3.
Therefore, the expected value of X for this probability function is 7/3.