I only need someone to check my answers.
Find the expected value of a random variable X having the following probability distribution:
x -15 -1 0 1 5 8
p (x=x) .12 .16 .28 .22 .12 .10
E(X) = (-5) * (.12) + (-1) *(.16) + (0) * (.28) + (1) * (.22) + (5) (.12) + (8) (.10) = .86
You evaluated E(X) correctly,
but not if the first data value is in fact -15, and not -5.
Oops i meant -5 for the table value.
To find the expected value of a random variable, you multiply each possible value of the random variable by its corresponding probability and sum them up.
In this case, you have the random variable X with the following probability distribution:
x -15 -1 0 1 5 8
p (x=x) .12 .16 .28 .22 .12 .10
To calculate the expected value E(X), you need to multiply each value of X by its corresponding probability and then sum them up.
E(X) = (-15) * (0.12) + (-1) * (0.16) + (0) * (0.28) + (1) * (0.22) + (5) * (0.12) + (8) * (0.10)
Now let's calculate it:
E(X) = (-15) * (0.12) + (-1) * (0.16) + (0) * (0.28) + (1) * (0.22) + (5) * (0.12) + (8) * (0.10)
= -1.80 - 0.16 + 0 + 0.22 + 0.60 + 0.80
= -0.34
So, the expected value of the random variable X is -0.34, not 0.86 as you calculated.