A random experiment has sample space S={a, b, c, d}S={a, b, c, d}. Suppose that P({a,...
A random experiment has sample space S={a, b, c, d}S={a, b, c, d}. Suppose that P({a, d})=38, P({a, b})=58P({a, d})=38, P({a, b})=58, and P({d})=18P({d})=18.
Use the axioms of probability to find the probabilities of each of the elementary events.
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A random experiment has sample space S={a, b, c, d}S={a, b, c,
d}. Suppose that P({a,...
Q2. 5 marks] The sample space of a random experiment is (a; b; c; d; e)...
Q2. 5 marks] The sample space of a random experiment is (a; b; c; d; e) with probabilities 0.1, 0.2, 0.2, 0.1, and 0.4 respectively. Let A denote the event fa; b; c) and let B denote the event (b; c; e a. Determine P(A | B') b. Are the events A and B independent?
The sample space of a random experiment is fa, b, c, d, e, f}, and each...
The sample space of a random experiment is fa, b, c, d, e, f}, and each outcome is equally likely. A random variable is defined as follows: b d Outcome C X 0 1.4 1.4 3 Determine the probability mass function of X. Use the probability mass function to determine the following probabilities. Give exact answers in the form of fraction a) P(X 1.4)= b) P(0.5<X< 2.7) c) P(X> 3) d) P(0 X 2) e) P(X 0 or X =...
Problem 2. Suppose the sample space S consists of the four points and the associated probabilities...
Problem 2. Suppose the sample space S consists of the four points and the associated probabilities over the events are given by P(cu 1)-0.2, P(ω2)-0.3, P(ag)-0.1, P(04)-0.4 Define the random variable X1 by and the random variable X2 by X2(2) 5, (a) Find the probability distribution of X1 (b) Find the probability distribution of the random variable X1 +X2 Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 0.8, determine K (b)...
5. Consider an experiment with sample space S and events A,B,C, and D with the following...
5. Consider an experiment with sample space S and events A,B,C, and D with the following probabil ities: P(AUB)-|, P(A) = P(čnD) = , P(C) = 훙 Furthermore, A and B are mutually exclusive (ie. A กั-o), while C and D are independent (ie. P(cr D) = P(C)P(D)). (Note: I know this looks like a lot of parts, but these are all short, quick answers!) (a) Find P(An (b) Find P(B) (c) Find P(AnB) (d) Find P(AUB) (e) Are A...
Consider an experiment with sample space S and events A,B,C, and D with the following probabl...
Consider an experiment with sample space S and events A,B,C, and D with the following probabl ities: P(AUB)-, P(A)- , P(Cn D) , PC)- . Furthermore, A and B are mutually exclusive (i.e. AnB-), while C and D are independent (i.e. P(CND) P(C)P(D)). Note: I know this looks like a lot of parts, but these are all short, quick answers!) ' (a) Find P(AnB (b) Find P(B) (c) Find P(A กั Bc). (d) Find P(AUBe) (e) Are A and B...
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B)...
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B) = 0.5 and P(A∩B) = 0.3. Express each of the following events in set notation and find the probability of each event: a) A or B occurs b) A occurs but B does not occur c) At most one of these events occurs
Let E and F be two events of an experiment with sample space S. Suppose P(E)= 0.4,...
Let E and F be two events of an experiment with sample space S. Suppose P(E)= 0.4, P(F)=0.3, P(E U F) =0.5, Find P(F|E) and determine if the two events are independent. A) P(F|E)= 3/4, E and F are independent. B) P(F|E)= 3/4, E and F are not independent. C) P(F|E)=1/2 , E and F are independent. D) P(F|E)= 1/2, E and F are not independent.
Question 2: The sample space of a random experiment is fabedef) such that the prob- ability...
Question 2: The sample space of a random experiment is fabedef) such that the prob- ability of each outcome is given in the following table: Outcome Probability 0.09 0.24 0.15 0.3 0.16 0.06 a. Consider the following events: C fa, c,d, f D-tb, d, e (a) What is the probability that event A occurs? (b) What is the probability that event D does not occur? (c) If event B occurs, what is the probability that event D occurs? (d) Are...
Probability: if the omega - {A,B,C} is the sample space for an experiment then P({A}) =...
Probability: if the omega - {A,B,C} is the sample space for an experiment then P({A}) = 1/3 (True or False?) explain. if the omega - {A,B,C} is the sample space for an experiment, then P({A,B}) = 1 (True or False?) explain. if a coin is tossed three times (and it is a fair coin) then the probability that H and T each come up at least once is 3/4 (True or False?) explain.
2. Show that P[AIB] satisfies the three axioms of probability b) PISIB] 1 for sample space S c) I...
2. Show that P[AIB] satisfies the three axioms of probability b) PISIB] 1 for sample space S c) If AnC 0 (empty set), then P[An CIB] P[AIB] + P[CIB]
2. Show that P[AIB] satisfies the three axioms of probability b) PISIB] 1 for sample space S c) If AnC 0 (empty set), then P[An CIB] P[AIB] + P[CIB]
Q2. 5 marks] The sample space of a random experiment is (a; b; c; d; e) with probabilities 0.1, 0.2, 0.2, 0.1, and 0.4 respectively. Let A denote the event fa; b; c) and let B denote the event (b; c; e a. Determine P(A | B') b. Are the events A and B independent?
The sample space of a random experiment is fa, b, c, d, e, f}, and each outcome is equally likely. A random variable is defined as follows: b d Outcome C X 0 1.4 1.4 3 Determine the probability mass function of X. Use the probability mass function to determine the following probabilities. Give exact answers in the form of fraction a) P(X 1.4)= b) P(0.5<X< 2.7) c) P(X> 3) d) P(0 X 2) e) P(X 0 or X =...
Problem 2. Suppose the sample space S consists of the four points and the associated probabilities over the events are given by P(cu 1)-0.2, P(ω2)-0.3, P(ag)-0.1, P(04)-0.4 Define the random variable X1 by and the random variable X2 by X2(2) 5, (a) Find the probability distribution of X1 (b) Find the probability distribution of the random variable X1 +X2 Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 0.8, determine K (b)...
5. Consider an experiment with sample space S and events A,B,C, and D with the following probabil ities: P(AUB)-|, P(A) = P(čnD) = , P(C) = 훙 Furthermore, A and B are mutually exclusive (ie. A กั-o), while C and D are independent (ie. P(cr D) = P(C)P(D)). (Note: I know this looks like a lot of parts, but these are all short, quick answers!) (a) Find P(An (b) Find P(B) (c) Find P(AnB) (d) Find P(AUB) (e) Are A...
Consider an experiment with sample space S and events A,B,C, and D with the following probabl ities: P(AUB)-, P(A)- , P(Cn D) , PC)- . Furthermore, A and B are mutually exclusive (i.e. AnB-), while C and D are independent (i.e. P(CND) P(C)P(D)). Note: I know this looks like a lot of parts, but these are all short, quick answers!) ' (a) Find P(AnB (b) Find P(B) (c) Find P(A กั Bc). (d) Find P(AUBe) (e) Are A and B...
Question 2: The sample space of a random experiment is fabedef) such that the prob- ability of each outcome is given in the following table: Outcome Probability 0.09 0.24 0.15 0.3 0.16 0.06 a. Consider the following events: C fa, c,d, f D-tb, d, e (a) What is the probability that event A occurs? (b) What is the probability that event D does not occur? (c) If event B occurs, what is the probability that event D occurs? (d) Are...
2. Show that P[AIB] satisfies the three axioms of probability b) PISIB] 1 for sample space S c) If AnC 0 (empty set), then P[An CIB] P[AIB] + P[CIB]
2. Show that P[AIB] satisfies the three axioms of probability b) PISIB] 1 for sample space S c) If AnC 0 (empty set), then P[An CIB] P[AIB] + P[CIB]
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