Sam keeps a record of his work outs over several years. x is the number of times he goes to the gym in a week. he calculates relative frequencies to create the empirical probability distribution below. x 0 1 2 3 4 p(x) 0.1 0.15 0.40 0.25 0.10 for example, for 10% of the weeks he did not go to the gym. for 15% of the weeks he went to the gym once. what is the mean of x (the expected number of times he visits the gym per week in the long run)?

2.1

Step-by-step explanation:

We know that for a discrete  random variable X, the expected value of X is given by E(X) = , where the values are the different values that can be taked by X, and is the probability mass function of X. In other words, if the discrete random variable X can take n different values with probabilities respectively, then, the expected value of X is given by E(X) =

So, in this case we have that the expected number of times that Sam visits the gym per week in the long run is given by

E(X) = (0)(0.1) + (1)(0.15) + (2)(0.4) + (3)(0.25) + (4)(0.1) = 2.1

34

step-by-step explanation: