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Statistics and Probability
# 3. Monty-Hall 10-doors (modified).
Consider the following modified Monty-Hall game with 10 doors.
Step 1: you choose one door at random.
Step 2: Monty opens 7 (out of 9 doors) that do not have the prize.
Step 3: you either stick with your original choice, or choose between one of the two unopened doors.
Set up the experiment two functions "monty_10doors_mod_noswitch" and "monty_10doors_mod_switch" (these functions will have no input values):
```{r}
monty_10doors_mod_noswitch <- function(){
}
monty_10doors_mod_switch <- function(){
}
Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
The computation of the theoretical probability in this case might not be completely obvious, however, use your empirical probability to make a guess.
```{r}
```
Not for submission: Play with this modified setup, for example Monty opens 6 doors at step 2 e
Consider the following modified Monty-Hall game with 10 doors.
Step 1: you choose one door at random.
Step 2: Monty opens 7 (out of 9 doors) that do not have the prize.
Step 3: you either stick with your original choice, or choose between one of the two unopened doors.
Set up the experiment two functions "monty_10doors_mod_noswitch" and "monty_10doors_mod_switch" (these functions will have no input values):
```{r}
monty_10doors_mod_noswitch <- function(){
}
monty_10doors_mod_switch <- function(){
}
Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
The computation of the theoretical probability in this case might not be completely obvious, however, use your empirical probability to make a guess.
```{r}
```
Not for submission: Play with this modified setup, for example Monty opens 6 doors at step 2 e
Statistics and Probability
Repeat the Monty Hall experiment now with 10 doors. Recall the game is as follows:
Step 1: you choose one door at random.
Step 2: Monty opens 8 (out of 9 doors) that do not have the prize.
Step 3: you either switch or don't switch.
Set up the experiment two functions "monty_10doors_noswitch" and "monty_10doors_switch" (these functions will have no input values):
```{r}
monty_10doors_noswitch <- function(){
}
monty_10doors_switch <- function(){
}
Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.
Step 1: you choose one door at random.
Step 2: Monty opens 8 (out of 9 doors) that do not have the prize.
Step 3: you either switch or don't switch.
Set up the experiment two functions "monty_10doors_noswitch" and "monty_10doors_switch" (these functions will have no input values):
```{r}
monty_10doors_noswitch <- function(){
}
monty_10doors_switch <- function(){
}
Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.
Statistics and Probability
the annual rainfall at a certain place is normally distributed with mean 30. If the rainfall during the past 8 years are 31.1, 30.7, 24.3, 28.1, 27.9, 32.2, 25.4 and 29.1, can we conclude that average rainfall during the past 8 years is less than the normal rainfall ?(LOS 1%)
Statistics and Probability
8.A survey of 800 families with 4 children each revealed the following distribution:No. of boys:01234No. of girls:43210No. of families:3217829023664Is this result consistent with the hypothesis that the male & female births are equallyprobable?
Statistics and Probability
A box of 10 light bulbs, 2 of which are faulty. A bulb is selected at random and put into a socket. If it works it is left there, if it is faulty it is discarded and a new bulb is selected. The process I continued until a bulb which works is found. Determine the probability distribution of X, the number of bulbs tried.
Statistics and Probability
Q1. A low noise transistor for use in computing products is being developed. It is claimed that the mean
noise level will be below the 2.5 dB level of the product currently in use.
a) Set up the appropriate null and alternative hypotheses for verifying the claim
b) A sample of 16 transistors yields x̅= 1.8 and s = 0.8. Find the P value for the test. Do you think
that H0 should be rejected? What assumptions are making concerning the distribution of the
random variable X, the noise level of a transistor?
c) Explain the context of this problem, what conclusions can be drawn regarding the noise level of
these transistors. If you make a Type I error, what will have occurred? What is the probability
that you are making such as error?
noise level will be below the 2.5 dB level of the product currently in use.
a) Set up the appropriate null and alternative hypotheses for verifying the claim
b) A sample of 16 transistors yields x̅= 1.8 and s = 0.8. Find the P value for the test. Do you think
that H0 should be rejected? What assumptions are making concerning the distribution of the
random variable X, the noise level of a transistor?
c) Explain the context of this problem, what conclusions can be drawn regarding the noise level of
these transistors. If you make a Type I error, what will have occurred? What is the probability
that you are making such as error?
Statistics and Probability
Assume that each time a metal detector at an airport signals, there is a 25% chance that the cause is
the change in the passenger’s pocket. During a given hour, 15 passengers are stopped because of a signal
signal from the metal detector.
a) Find the probability that at least 3 persons will have stopped due to change in their pockets.
b) If 15 passengers are stopped by the detector, would it be unusual for none of those to have been
stopped due to change in the pockets? Explain based on the probability of this occurring.
the change in the passenger’s pocket. During a given hour, 15 passengers are stopped because of a signal
signal from the metal detector.
a) Find the probability that at least 3 persons will have stopped due to change in their pockets.
b) If 15 passengers are stopped by the detector, would it be unusual for none of those to have been
stopped due to change in the pockets? Explain based on the probability of this occurring.
Statistics and Probability
A box of 10 light bulbs, 2 of which are faulty. A bulb is selected at random and put into a socket. If it works it is left there, if it is faulty it is discarded and a new bulb is selected. The process I continued until a bulb which works is found. Determine the probability distribution of X, the number of bulbs tried.
Statistics and Probability
You are a first-year student studying at a leading Business School and would like to study the annual packages offered to the students under management domain. To conduct this study, you went to the placement team and asked for related data. Placement team has provided you the data as follows:
Highest package offered = INR 20,00,000
Lowest package offered = INR 5,00,000
Also, you were informed that first-year salaries of management graduates is normally distributed with the population mean μ= INR 9,00,000 and the population standard deviation σ = INR 2,00,000. Find the probability of a randomly selected management graduate from the business school earning less than INR 7,00,000 annually
Statistics and Probability
In R studio
# 4. BONUS: Monty Hall with n-doors.
Repeat the Monty Hall experiment now with n doors. Recall the game is as follows:
Step 1: you choose one door at random.
Step 2: Monty opens n-2 (out of n-1 doors) that do not have the prize.
Step 3: you either switch or don't switch.
Set up the experiment two functions "monty_10doors_noswitch" and "monty_10doors_switch" (these functions will have input value as n):
```{r}
monty_ndoors_noswitch <- function(n){
}
monty_ndoors_switch <- function(n){
}
```
Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.
```{r}
```
# 4. BONUS: Monty Hall with n-doors.
Repeat the Monty Hall experiment now with n doors. Recall the game is as follows:
Step 1: you choose one door at random.
Step 2: Monty opens n-2 (out of n-1 doors) that do not have the prize.
Step 3: you either switch or don't switch.
Set up the experiment two functions "monty_10doors_noswitch" and "monty_10doors_switch" (these functions will have input value as n):
```{r}
monty_ndoors_noswitch <- function(n){
}
monty_ndoors_switch <- function(n){
}
```
Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.
```{r}
```
