Question

In: Advanced Math

5. Calculate the conditional probability distribution

|    | a1   | a2   |
|----|------|------|
| b1 | 0.37 | 0.16 |
| b2 | 0.23 | ?    |

5. Calculate the conditional probability distribution, ?(?|?)P(A|B).

6. Calculate the conditional probability distribution, ?(?|?)P(B|A).

7. Does ?(?|?)=?(?|?)P(A|B)=P(B|A)? What do we call the belief that these are always equal?

8. Does ?(?)=?(?|?)P(A)=P(A|B)? What does that mean about the independence of ? and B?

Solutions

Expert Solution


Related Solutions

Explain Probability Distribution of a single variable, Summary Measures of a Probability Distribution, Conditional Mean and...
Explain Probability Distribution of a single variable, Summary Measures of a Probability Distribution, Conditional Mean and Variance and Introduction to Simulation
Show that the conditional distribution of X, given X+Y=u (a value with positive probability, is binomial...
Show that the conditional distribution of X, given X+Y=u (a value with positive probability, is binomial with parameters (u, λ1/(λ1+λ2)
Conditional Probability Problem 1 Conditional probability In group of 200 university students, 140 are full time...
Conditional Probability Problem 1 Conditional probability In group of 200 university students, 140 are full time students (80 females and 60 males) and 60 no full time students (40 females and 20 males). Let    M=event a student is male    W=event a student is a female    F=event a student is full time    FC= event a student is not full time 1) Find the probability that a student is male and full time    2) Find the probability...
Simulating a conditional probability using R. Simulating the conditional probability P(A|B) requires repeated simulation of the...
Simulating a conditional probability using R. Simulating the conditional probability P(A|B) requires repeated simulation of the underlying random experiment, but restricting to trials in which B occurs. Suppose 3 dice are tossed and we want to find the probability of the first die is 4 given that the sum is 10. Modify the script ConditionalDice.R (you can find the R script file from Modules on this Canvas site) to find P(First die is 4 | Sum is 10) Hint: the...
Calculate the Probability *Binomial Distribution* An insurance company sells life insurance policies to 5 people with...
Calculate the Probability *Binomial Distribution* An insurance company sells life insurance policies to 5 people with the same age (35) and the same health condition (Excellent). If the Insurance company was estimating at 66% the probability of a person of that age and health condition should live 30 more years. What is the probability that 30 years after buying the policy: a. All 5 are alive b. 4 out of 5 have died c. No more than 3 survive d....
In probability theory, a conditional probability measures the probability of an event given another event has...
In probability theory, a conditional probability measures the probability of an event given another event has occurred. The conditional probability of A given B, denoted by P(A|B), is defined by P(A|B) = P(A ∩ B) P(B) , provided P(B) > 0. Show that the conditional probability defined above is a probability set function. That is show that a) P(A|B) ≥ 0 [4 Marks] b) P(S|B) = 1. [4 Marks] c) P( S Ai |B) = PP(Ai |B) [4 Marks]
Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of...
Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being 0.50 and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =  Comparison: Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being 0.10 and n = 10. Write a comparison of these statistics to those...
Consider a hyper geometric probability distribution with n=7, R= 8 and N=17 a) calculate P(x =5)...
Consider a hyper geometric probability distribution with n=7, R= 8 and N=17 a) calculate P(x =5) b) calculate P(x=4) c) calculate P(x <=1) d) calculate the mean and strandard deviation of this distribution
Use the Central Limit Theorem to calculate the following probability. Assume that the distribution of the...
Use the Central Limit Theorem to calculate the following probability. Assume that the distribution of the population data is normally distributed. A person with “normal” blood pressure has a diastolic measurement of 75 mmHg, and a standard deviation of 4.5 mmHg. i) What is the probability that a person with “normal” blood pressure will get a diastolic result of over 80 mmHg, indicating the possibility of pre-hypertension? ii) If a patient takes their blood pressure every day for 10 days,...
Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls...
Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls for a total of 13 balls. If 5 balls are randomly selected without replacement what is the probability of selecting at least two red balls given that at least one yellow ball is selected? a) 0.59 b) 0.61 c) 0.63 d) 0.65 e) 0.67
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT