Suppose you toss a fair coin 10 times resulting in a sequence of heads (H) and tails (T). Let X be the number of times that the sequence HT appears. For example, HT appears thrice in THTHHTHHHT Find E(X). Hint: Use Indicator random variables.

Step-by-step explanation:

When it comes to statistics and probability, a random variable is a numerical explanation of the result of experimentation in statistics and probability. For a distinct random variable, x, the probability distribution is described by a probability mass function, which is denoted by f(x). This function offers the probability for every value of the random variable.

The step by step workings have all been explained in the attached image below

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.