You have 3 coins that look identical, but one is not a fair coin. The probability the unfair coin show heads when tossed is 3/4, the other two coins are fair and have probability 1/2 of showing heads when tossed.
You pick one of three coins uniformly at random and toss it n times, (where n is an arbitrary fixed positive integer).
Let Y be the number of times the coin shows heads. Let X be the probability the coin you choose shows heads when flipped. (Note that X is a random variable because you’re randomly choosing a coin).
a) What is the pmf of X?
b) For each x that the random variable X can equal, give the conditional distribution of Y given X = x.
c) Determine the unconditional distribution of Y
d) Compute the expectation of Y

Sanya noticed that the temperature was falling at a steady rate of 1.4 degrees every hour from the time that she first checked her outdoor thermometer. by 6 a.m., the temperature had fallen 21 degrees. which expression can you use to find how many hours earlier she had first checked the thermometer?

Students at a high school were asked about their favorite outdoor activity. the results are shown in the two-way frequency table below. fishing camping canoeing skiing total boys 36 44 13 25 118 girls 34 37 22 20 113 total 70 81 35 45 231 select all the statements that are true based on the given table. more girls chose camping as their favorite outdoor activity than boys. more girls chose canoeing as their favorite outdoor activity than those who chose skiing. more boys chose skiing as their favorite outdoor activity than girls. there were more boys surveyed than girls. twice as many students chose canoeing as their favorite outdoor activity than those who chose fishing. more students chose camping as their favorite outdoor activity than the combined number of students who chose canoeing or skiing.

The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. the support post is 8 ft tall. the distance from the front of the house to the support post is less than the distance from the post to the back of the house. how far from the front of the house is the support post positioned?