Problem 9.1 A gatekeeper stands in front of a locked door. He has a keychain with...

Question:

Problem 9.1 A gatekeeper stands in front of a locked door. He has a keychain with 12 keys and a single one of them unlocks the door in front of him. (a) First assume that he tries the keys one after the other. Let X be the random variable that describes the number of unsuccessful attempts at unlocking the door in this case. (i) Let X(12) denote all the possible values that X can take. Determine X(22). (ii) What is the probability that P(X = 0)? P(X = 1)? P(X = k) for any k e X(22)? (iii) Determine the expected number of failed attempts. (b) Assume now that it is very cold and dark. The gatekeeper therefore drops the keychain after each failed attempt, and he no longer knows which key he has already tried. Let Y be the random variable that describes the number of unsuccessful attempts at unlocking the door in that case. (i) Determine the distribution of Y. (ii) What is the cumulative distribution function of Y? (iii) What is the probability that he will need more than 12 attempts? (iv) What is the expected number of attempts? (v) What is the expected number of failed attempts?

Similar Solved Questions

Me Remaining (Minutes): 33 The patient reports having a severe headache when taking nitroglycerin (Nitrostat )...
me Remaining (Minutes): 33 The patient reports having a severe headache when taking nitroglycerin (Nitrostat ) for angina. The nurse tells the patient that the headache is caused by a. aura prior to a migraine headache. b. hypoglyemia. c. vasoconstriction of the cerebral arteries. Od. vasodilation o...
3. (4 +3 +3 +2- 12 pts) 3R Fig.1 Fig.2 (i) The resistance R in the...
3. (4 +3 +3 +2- 12 pts) 3R Fig.1 Fig.2 (i) The resistance R in the circuit in Fig. 1 is R 102 . What is the emf, E, of the battery if the current in the 3R resistor is 2.0 A? . What is the current in the battery? (ii) We replace the 3R resistor by a capacitor C = 135 μF, see Fig. 2. . What is the...
Answer true or false Which statements are true for two oppositely charged, isolated parallel plates: C=capacitance,...
answer true or false Which statements are true for two oppositely charged, isolated parallel plates: C=capacitance, U-stored energy (Q and-Q-charge on the plates). Note: Isolated plates čan not lose their charge Inserting a dielectric increases C Inserting a dielectric increases Q. when the dis...
Question 9 X.X = X True False Question 10 The Boolean function Flx, y, z) =...
Question 9 X.X = X True False Question 10 The Boolean function Flx, y, z) = (y + x)(y + x)(y'+z) is equivalent to: yz y'z + xyz + xyz O y'z+xz X...
For the figure, what is the moment caused by the two forces F1 and Fall about...
For the figure, what is the moment caused by the two forces F1 and Fall about a line starting at point P and extending to point Q? Use a Cartesian vector approach to solve this problem. Hint: It would be easier to find the resultant vector first, but it is not necessary Given: F1 F1= (2881 +691j -75...
A 5.4 kg cat and a 2.3 kg bowl of tuna fish are at opposite ends...
A 5.4 kg cat and a 2.3 kg bowl of tuna fish are at opposite ends of the 4.0-m-long seesaw. (Figure 1) Part A: How far to the left of the pivot must a 3.8 kg cat stand to keep the seesaw balanced? 2.0 m 2.0 m...
Using the Profitability Index rule, which of the four projects is the best investment? Project NPV...
Using the Profitability Index rule, which of the four projects is the best investment? Project NPV Investment A $2.3 mil$ 5.2 mil B $1.2 mil$ 2.8 mil C $3.5 mil$ 6.9 mil D $4.4 mil$ 8.9 mil Multiple Choice Project A Project B Project C Project D...
List three direct variable costs you would find in a cell phone charger manufacturing business. Be...
List three direct variable costs you would find in a cell phone charger manufacturing business. Be specific, do not respond in general terms.: List three overhead costs you would find in a cell phone charger manufacturing business. Be specific, do not respond in general terms.: List three period cos...
Two long (infinite) wires are placed in the x-y plane parallel to one another. One is...
Two long (infinite) wires are placed in the x-y plane parallel to one another. One is placed on the x axis and the current in that wire is 14 amps running in the +x direction. The other wire is placed at y = +2.6 meters (2.6 meters "above" the first wire, in the x-y plane). The second wire h...
Write a program that computes the average and standard deviation of four scores. The standard deviation...
Write a program that computes the average and standard deviation of four scores. The standard deviation is defined to be the square root of the average of the four values. Use two functions. One function to calculate the average, this function should be with Return Type "double". Second Func...
272 is incorrect Scenario 5.6: Consider the information in the table below, describing choices for a...
272 is incorrect Scenario 5.6: Consider the information in the table below, describing choices for a new doctor. The outcomes represent different macroeconomic environments, which the individual cannot predict. We assume the doctor's utility of income function is given as: U(1) = 10.5, where ...
Which of the following situations would suggest that a patient has a common law right to...
Which of the following situations would suggest that a patient has a common law right to hospital admission? Group of answer choices Entry of the hospital through the emergency room Using a physician who is a member of the hospital’s medical staff Having been previously admitted and discharged...