a) Mrs Legodi, a registered student at the University of Limpopo, tossed a fair coin three times. She decided to let X to be a random variable that takes the value 1 if the outcome of a toss is a head and the value 0 otherwise. She also defined Y to be a random variable of the total number of heads in the three tosses. i) What will be her joint probability mass function (PMF) of X and Y?
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- create a probability model for random variable Z, Z = the number of heads that occur in the last two tosses whenever you toss a coin 4 times.An Engineer has a duty of conducting compressive strength test for 50 concrete cubes. 40 cubes passed the test successfully and 10 cubes failed in the test. If 5 cubes are selected at random by the engineer to be inspected, determine the probability that the selected concrete cubes exactly include 4 cubes passed and 1 cube :failed? Choose the correct answer 0.254 O 0.334 O 0.678 O 0.112 O 0.431 OA balanced die is rolled twice in a row. Given that the first roll was a 3, what is the probability that the sum of the two results is greater than 6?
- An urn consists of 3 green balls, 4 blue balls, and 6 red balls. In a random sample of 5 balls, find the probability that 2 blue balls and at least 1 red ball are selected. The probability that 2 blue balls and at least 1 red ball are selected is (Round to four decimal places as needed.)There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.Of the 45 students enrolled in a statistics class last semester, 21 received a high grade and 24 used the recommended textbook. 10 of those who used the recommended textbook also received a high grade. Report answers accurate to 4 decimal places. What is the probability that a randomly selected student from the class: a) did not use the recommended textbook?b) used the recommended textbook but did not receive a high grade?c) either used the recommended textbook or received a high grade?d) neither received a high grade nor used the recommended textbook? If two students were selected from the class, one after the other and without replacement, what is the probability that: a) the second student used the recommended textbook given the first student also did?b) the second student used the recommended textbook given the first did not?c) both students used the recommended textbook?d) only the second student received a high grade?e) only one of the two students received a high grade?f)…
- An urn contains 4 identical balls number from 1 to 4. Two balls will be taken from urn with replacement and define the random variable w as the maximum of two numbers obtained. Give the probability mass function of a and its bar plot.The time between busses on Stevens Creek Blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes. Find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.When rolling a die 114 times, what is the probability of rolling a 6 greater than 20 times? Question 6 options: 1) 0.0948 2) 0.4395 3) 0.3447 4) 0.0474 5) 0.6553
- Faults occur on a piece of string at an average rate of one every three metres. Bobbins, each containing 5 metres of this string are to be used. What is the probability that a randomly selected bobbin will contain (a) two faults. (b) at least two faults.How was the correct answer of 0.0741 attained?a box contains 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?