A coin with probably of heads = 1/2 is tossed over and over. X is defined as the number of tosses needed to obtain the pattern: heads, heads (a toss that results in heads is followed by heads on the next toss).

a. Find the probability mass function of X

b. find the expected value of X.

1616​%

adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ (a) exactly​ three, (b) at least​ four, (c) less than eight.

26​% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ (a) exactly​ three, (b) at least​ four, (c) less than eight?

A sample of ten items is selected without replacement from a group of 200 object 40 of which are defective.  What is the probability that this sample will contain three defective items?

And Solve using R for number of defective items in the sample being 0, 1, 2,3, …, 10. Graph the distribution.

A coin with probably of heads = 1/2 is tossed over and over. X is defined as the number of tosses needed to obtain the pattern: heads, tails (a toss that results in heads is followed by tails on the next toss).

a. Find the probability mass function of X

b. find the expected value of X.

c) Patients arrived at hospital emergency department follows a Poisson distribution with a mean of 4 patients per hour.

i. In any 90 minutes period of time, find the probability that exactly 10 patients arrived.

ii. Find the standard deviation of the number of patients arriving at the hospital.

Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random. Define the random variable XX as the number of defective cameras in the sample.

Write the probability distribution for XX.

What is the expected value of XX?

37​% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ (a) exactly​ three, (b) at least​ four, (c) less than eight.

A cube is painted on the outside, then cut into 27 equally sized pieces in a 3^3 format. Let X = the total number of painted sides when the 27 pieces are put in a bag and two pieces are randomly selected. Find the probability mass function, the expected value, and the variance of X