The outcomes of an experiment and the probability of each outcome are given in the table below. Compute the expectation for this experiment.
Outcome Probability
5 0.4
6 0.31
7 0.1
8 0.08
9 0.06
10 0.05
To compute the expectation for this experiment, we multiply each outcome by its corresponding probability and sum them up.
E(X) = 5*0.4 + 6*0.31 + 7*0.1 + 8*0.08 + 9*0.06 + 10*0.05
= 2 + 1.86 + 0.7 + 0.64 + 0.54 + 0.5
= 6.24
Therefore, the expectation for this experiment is 6.24.
To compute the expectation for this experiment, we need to multiply each outcome by its corresponding probability and sum up the results.
Step 1: Multiply each outcome by its probability:
(5 * 0.4) + (6 * 0.31) + (7 * 0.1) + (8 * 0.08) + (9 * 0.06) + (10 * 0.05)
Step 2: Calculate the products:
2 + 1.86 + 0.7 + 0.64 + 0.54 + 0.5
Step 3: Sum up the products:
5.24
Therefore, the expectation for this experiment is 5.24.