Final answer:
The random variable X equals 2s, where s belongs to the sample space S = {0, 1, 2.5, 6}. The possible values of X are {0, 2, 5, 12}, and since each event is equally likely, each has a probability of 0.25. The probability distribution of X can be sketched as a bar graph with these probabilities.
Step-by-step explanation:
Given a sample space S = {0, 1, 2.5, 6} and the random variable X defined as X = 2s, where s is an element of the sample space, we first find the possible values X can take on by substituting each element of S into the given formula:
- For s=0, X = 2*0 = 0
- For s=1, X = 2*1 = 2
- For s=2.5, X = 2*2.5 = 5
- For s=6, X = 2*6 = 12
As all elements in the sample space are equally likely, each value of X has a probability of 1/4. To sketch the probability distribution of X, we create a bar graph with the values of X on the x-axis and their corresponding probabilities on the y-axis.
The requested calculations for parts b, c, and d of the question seem to be referring to a different scenario absent in this question, and thus cannot be addressed without additional context. For the sketch of the probability distribution of X, we only require the random variable's definition and the sample space provided.