Homework Answers
Given that the events E and F are disjoint (mutually exclusive).
This gives . Also P(E) = p and P(F) = q.
To find: Probability that E will occur before F
Assume that the experiment is repeated for n times and the event E occurs in the n th trial. Then there are (n-1) failures before that. So the probaility of event E occuring before F is equivalent in obtaining
The above value is the answer to the question.
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Assume that events (E, F) are disjoint, and their probabilities are specified as (here p. An...
Problem 7: 10 points Assume that events (E, F) are disjoint, and their probabilities are specified...
Problem 7: 10 points Assume that events (E, F) are disjoint, and their probabilities are specified as (here p+q1). An experiment is repeated until either E or F will occur Find the probability that E will occur before F Hint Introduce a random variable, N, which is the first occurrence of EUF. Then express the probability that E occurs before F, given that EUF occurs at the time and use the formula where A is the desired event.
show all the work 2. Let E, F be events with probabilities P(E) = 2, P(F)...
show all the work
2. Let E, F be events with probabilities P(E) = 2, P(F) = 3, PENF) = .1. Compute the probability that at most one of E, F occurs. A. .4 B..5 C..1 D..9
1. Suppose that A, B, and C are events such that P[A]- PB0.3, PC 0.55, PIANB]-...
1. Suppose that A, B, and C are events such that P[A]- PB0.3, PC 0.55, PIANB]- For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint regions in the diagram before starting...
I need answer for example 1 . the probabilities of occurrence of these events are, respectively,...
I need answer for example 1 .
the probabilities of occurrence of these events are, respectively, p and (1-p). Let X denotes the number of successes. Here X can take the values 0 or 1. X is said to have a Bernoulli distribution. Definition: random variables X is said to have a Bernoulli distribution and is referred to as a Bernoulli random variable, if and only if its probability distribution is given by P(X = x) = p4" for x...
1. Let (S;F;P) be a probability space with A 2 F and B 2 F such...
1. Let (S;F;P) be a probability space with A 2 F and B 2 F such that P(A) = 0:3 and P(B) = 0:4. Find the following probabilities under the specified conditions. Note that I don’t expect you to have to show much work in answering this question. (a) either A or B occurs if A and B are mutually exclusive (b) either A or B occurs if A and B are statistically independent (c) either A or B occurs...
l. Suppose that A, B, and C are events such that PLA] = P[B] = 0.3,...
l. Suppose that A, B, and C are events such that PLA] = P[B] = 0.3, P[C] = 0.55, P[An B] = For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. (Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint...
Q3.2 Let (12, F,P) be a probability space. Decide whether each of the following statements hold....
Q3.2 Let (12, F,P) be a probability space. Decide whether each of the following statements hold. (i) 0 is independent of ), and N is independent of 12; (ii) If E is any event which is independent of itself, then either E = 0 or E = N; (iii) If E is any event which is independent of itself, then either P(E) = 0 or P(E) = 1; (iv) If events A and B are both disjoint and independent, then...
It is proposed to model the onset of hurricanes anywhere in the Gulf of Mexico as...
It is proposed to model the onset of hurricanes anywhere in the Gulf of Mexico as a Poisson process. The rate of occurrence, however, depends strongly on the month of the year. Specifically, we assume that hurricanes occur in only three months of the year: August, September, and October. During these months, the mean hurricane occurrence rate per month is as follows: Month Mean occurrence rate August 1.0 event per month September 2.0 events per month October 1.0 event per...
Q1) Consider two events P and Q. a. Write the general formula used to calculate the probability that either event P occu...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
1. Consider a statistical experiment E: (, F,P) and an event A . Note: A EF....
1. Consider a statistical experiment E: (, F,P) and an event A . Note: A EF. a. Use the axioms of probability to show that P(A) 1-P(A). b. Repeat (a) using the definition of the σ-field. 2. Consider a statistical experiment E: (, F,P) in which a fair coin is flipped successively until the same face is observed on successive flips. Let A = {x: x = 3, 4, 5, . . .); that is, A is the event that...
Problem 7: 10 points Assume that events (E, F) are disjoint, and their probabilities are specified as (here p+q1). An experiment is repeated until either E or F will occur Find the probability that E will occur before F Hint Introduce a random variable, N, which is the first occurrence of EUF. Then express the probability that E occurs before F, given that EUF occurs at the time and use the formula where A is the desired event.
show all the work
2. Let E, F be events with probabilities P(E) = 2, P(F) = 3, PENF) = .1. Compute the probability that at most one of E, F occurs. A. .4 B..5 C..1 D..9
1. Suppose that A, B, and C are events such that P[A]- PB0.3, PC 0.55, PIANB]- For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint regions in the diagram before starting...
I need answer for example 1 .
the probabilities of occurrence of these events are, respectively, p and (1-p). Let X denotes the number of successes. Here X can take the values 0 or 1. X is said to have a Bernoulli distribution. Definition: random variables X is said to have a Bernoulli distribution and is referred to as a Bernoulli random variable, if and only if its probability distribution is given by P(X = x) = p4" for x...
l. Suppose that A, B, and C are events such that PLA] = P[B] = 0.3, P[C] = 0.55, P[An B] = For each of the events given below in parts (a)-(d), do the following: (i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (ii) Evaluate the probability of the event. (Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoint...
Q3.2 Let (12, F,P) be a probability space. Decide whether each of the following statements hold. (i) 0 is independent of ), and N is independent of 12; (ii) If E is any event which is independent of itself, then either E = 0 or E = N; (iii) If E is any event which is independent of itself, then either P(E) = 0 or P(E) = 1; (iv) If events A and B are both disjoint and independent, then...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
1. Consider a statistical experiment E: (, F,P) and an event A . Note: A EF. a. Use the axioms of probability to show that P(A) 1-P(A). b. Repeat (a) using the definition of the σ-field. 2. Consider a statistical experiment E: (, F,P) in which a fair coin is flipped successively until the same face is observed on successive flips. Let A = {x: x = 3, 4, 5, . . .); that is, A is the event that...
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