Sage-Tips

When 4 coins are tossed the value of random variable number of heads is?

In counting the number of heads in 4 coin flips, the probability that we get exactly one head is the probability that we get anyone of the following 4 outcomes: HTTT, THTT, TTHT, or TTTH. Each has probability 1/16, so the probability to get exactly one head in 4 flips is 1/16 + 1/16 + 1/16 + 1/16 = 4/16 = 1/4.

What are the possible value of a random variable for the number of heads?

X = “The number of Heads” is the Random Variable. In this case, there could be 0 Heads (if all the coins land Tails up), 1 Head, 2 Heads or 3 Heads. But this time the outcomes are NOT all equally likely.

What is the probability of getting at least one tail when four coins are tossed at the same time illustrate your answer?

Answer is 15/16. This is because there are total of 16 out comes and there is only one out comr in which there is no tail (h h h h) remaining 15 are favorable out comes.

What is the value of the random variable Z?

A random variable has a probability distribution that represents the likelihood that any of the possible values would occur. Let’s say that the random variable, Z, is the number on the top face of a die when it is rolled once. The possible values for Z will thus be 1, 2, 3, 4, 5, and 6.

What is not a random variable?

A non-random variable is generally called a Constant.

How do you define a random variable?

A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be either discrete (having specific values) or continuous (any value in a continuous range).

How many coins are tossed when the random variable is Z?

EXERCISES 1.Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. Possible Outcomes Value of the Random Variable Z TTTT 0 TTTH 1 TTHT 1 THTT 1 HTTT 1 TTHH 2 THTH 2 THHT 2 HHTT 2 HTTH 2 HTHT 2 HTHH 3 THHH 3 HHTH 3 HHHT 3 HHHH 4

How many coins are tossed in a coin toss?

Four coins are tossed. Let y be the random variable representing the number of tails that occur. What are the values of the random variables? You mean “What values can y take?” The answer is that you can have no tails, four tails and all the whole numbers in between. There is no rocket science here.

What are the possible values of the random variable z?

Hence, the random variable Z takes any one value from {0,1,2,3,4}. The possible values of the random variable Z are 0,1,2,3, and 4. You did not ask about the probability distribution so that is all that needs to be said. It is simple with 4 coins one can have maximum 4 heads.

What is the value of z=1 in this case?

Z is the random variable representing the number of heads that occur. We want to find all possible values of Z. All the four outcomes are ‘Tail’. So the number of heads is 0. Hence, Z=0 in this case. Any 3 of the 4 outcomes are ‘Tail’ and the remaining one is a ‘Head’ Hence, Z=1 in this case.