Example #2:
A die is rolled. Assume that a random variable X represents the outcomes of this experiment. Construct a probability distribution table and represent this probability distribution graphically. (Use the x-axis for values of X and the y-axis for P(X)).
Example #3:
A coin is tossed 3 times. Suppose that the random variable X is defined as the number of heads. Construct a probability distribution of X and represent this probability distribution graphically. (Use the x-axis for values of X and the y-axis for P(X)).
Example 2:
Outcome X (Number appear on die after rollling it) | 1 | 2 | 3 | 4 | 5 | 6 |
Probability P(X) | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 |
Example 3:
Outcome | HHH | HHT | HTH | HTT | THH | THT | TTH | TTT |
X (Number of Heads) | 3 | 2 | 2 | 1 | 2 | 1 | 1 | 0 |
X | 0 | 1 | 2 | 3 |
P(X) | 1/8 | 3/8 | 3/8 | 1/8 |
A die is rolled. Assume that a random variable X represents the outcomes of this experiment
A coin is tossed three times. X is the random variable for the number of heads occurring. a) Construct the probability distribution for the random variable X, the number of head occurring. b) Find P(x=2). c) Find P(x³1). d) Find the mean and the standard deviation of the probability distribution for the random variable X, the number of heads occurring.
Let random variable x represent the number of heads when a fair coin is tossed two times. a) construct a table describing probability distribution b) determine the mean and standard deviation of x (round to 2 decimal places)
A fair tetrahedron (four-sided die) is rolled twice. Let X be the random variable denoting the total number of dots in the outcomes, and Y be the random variable denoting the maximum in the two outcomes. Thus if the outcome is a (2, 3) then X = 5 while Y = 3. (a) What are the ranges of X and Y ? (b) Find the probability mass function (PMF) of X and present it graphically. Describe the shape of this...
explainhow to solve Example 33: A die is rolled, find the probability that an even number is obtained. Example 34: Two coins are tossed, find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tils) Example 35: Two dice are rolled, find the probability that the sum is a) equal to 1 b) equal to 4 c) less than 13
Please answer questions a b and c I0 a) If a fair die is rolled 22 times, what is the probability that a 6 is obtained exactly 3 times? (b) If a fair die is rolled, what is the probability that the third time that a 6 is obtained is on the tenth roll? (c) If a fair coin is tossed 11 times, what is the prob ability that three or fewer heads are obtained?
2. Assume two fair dice are rolled. Let X be the number showing on the first die and number showing on the second die. (a) Construct the matrix showing the joint probability mass function of the pair X,Y. (b) The pairs inside the matrix corresponding to a fixed value of X - Y form a straight line of entries inside the matrix. Draw those lines and use them to construct the probability mass function of the random variable X-Y- make...
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (o) which we write hth, int, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hu, then r (11)=2. Suppose that the random variable x is defined in terms of r as follows: X-6R-2R2-3. The values of x are thus: Outcome h ht|th ththhhttthhth htt Value of ΧΙ...
A coin is tossed three times and a Random variable X represents the total number of tails obtained. Then possible values of X are:
Construct a tree diagram of a probability experiment where a 6-sided die is rolled, and then a coin is flipped. a. The probability that there was a number greater than 3 and a tail on the coin. b. The probability that there was an even number on the dies and a tail on the coin. Show all the calculation steps
Find the standard deviation of the binomial random variable. A die is rolled 16 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.