9. There is a 0.8 probability that the temperature will be below freezing on

any winter's day in Toronto. Given that the temperature is below freezing

my car fails to start 15 percent of the time. Given that the temperature is

above freezing my car fails to start 5 percent of the time. Given that my

car starts, what is the probability that the temperature is below freezing?

10. If a baseball player is hitting .250 (i.e., if averages one hit per four times

at bat), how many times will he have to come up to bat to have a 90%

chance of getting a hit? Hint: Ask yourself what the probability is of not

getting a hit in n times at bat. Then take advantage of the fact that the

event 'getting at least one hit in n times at bat' is the complementary event

to the event of 'not getting a hit in n times at bat'.

11. A particular automatic sprinkler system for high-rise apartment buildings, office buildings, and hotels has two different types of activation devices

on each sprinkler head. One type has a reliability of .91 (i.e., the probability that it will activate the sprinkler when it should is .91). The other

type, which operates independently of the first type, has a reliability of .87.

Suppose a serious fire starts near a particular sprinkler head.

a) What is the probability that the sprinkler head will be activated?

b) What is the probability that the sprinkler head will not be activated?

c) What is the probability that both activation devices will work properly?

d) What is the probability that only the device with reliability .91 will

work properly

(F) What is the 95% confidence interval of the mean time people wait before

farting in front of a romantic partner.

Animal Research (AR) case study

29. (AR) What percentage of the women studied in this sample strongly agreed

(gave a rating of 7) that using animals for research is wrong?

30. (AR) Use the proportion you computed in #29. Compute the 95% confidence

interval on the population proportion of women who strongly agree that animal

research is wrong.

31. (AR) Compute a 95% confidence interval on the difference between the gender

means with respect to their beliefs that animal research is wrong.

ADHD Treatment (AT) case study

32. (AT) What is the correlation between the participants' correct number of

responses after taking the placebo and their correct number of responses after

taking 0.60 mg/kg of MPH? Compute the 95% confidence interval on the

population correlation.

Weapons and Aggression (WA) case study

33. (WA) Recall that the hypothesis is that a person can name an aggressive word

more quickly if it is preceded by a weapon word prime than if it is preceded by

a neutral word prime. The first step in testing this hypothesis is to compute the

difference between (a) the naming time of aggressive words when preceded by

a neutral word prime and (b) the naming time of aggressive words when

preceded by a weapon word prime separately for each of the 32 participants.

That is, compute an - aw for each participant.

a. (WA) Would the hypothesis of this study be supported if the difference were

positive or if it were negative?

b. What is the mean of this difference score?

c. What is the standard deviation of this difference score?

d. What is the 95% confidence interval of the mean difference score?

1. Input signal X = {-5, 5} is sent via a noisy communication channel (variance of noise is not known). If we know that SNR is 30 dB, what is the value of the variance of the noise? 2. Input signal X = {-5, 5} is sent via a noisy communication channel (variance of noise is known to be 0.1). What is the resulting SNR (in dB)? 3. Derive an expression for probability of a bit error in terms of E[N']. Given input signal X = {-5, 5} is sent via a noisy communication channel (variance of noise is not known). 4. Derive an expression for probability of a bit error in terms of SNR. 5. Given that SNR is 12 dB, find the probability of a bit error. 6. Find SNR (in dB) given that probability of a bit error is known to be 0.001.ADH 5. An insurance company sells automobile liability and collision insurance. Let X denote the percentage of liability policies that will be renewed at the end of their terms and Y the percentage of collision policies that will be renewed at the end of their terms. Given that * and Y have joint cumulative distribution function: xy(x+y) F(x, y) = { 2,000,000' 0 x $ 100,0 sys 100 otherwise calculate Var X. A) 764 833 C) 3402May 15. 2019 5. Use the joint cumulative distribution function to answer the questions below. (24 points) 0 Fx.Y(x,y) = 2