diff --git a/06_StatisticalInference/homework/hw1.Rmd b/06_StatisticalInference/homework/hw1.Rmd index 7f31c63a0..f5476f5c7 100644 --- a/06_StatisticalInference/homework/hw1.Rmd +++ b/06_StatisticalInference/homework/hw1.Rmd @@ -40,22 +40,22 @@ Creating Data Products --- &radio -Consider influenza epidemics for two parent heterosexual families. Suppose that the probability is 15% that at least one of the parents has contracted the disease. The probability that the father has contracted influenza is 6% while that the mother contracted the disease is 5%. What is the probability that both contracted influenza expressed as a whole number percentage? +Consider influenza epidemics for two parent heterosexual families. Suppose that the probability is 15% that at least one of the parents has contracted the disease. The probability that the father has contracted influenza is 10% while that the mother contracted the disease is 9%. What is the probability that both contracted influenza expressed as a whole number percentage? 1. 15% -2. 6% -3. 5% -4. _2%_ +2. 10% +3. 9% +4. _4%_ *** .hint -$A = Father$, $P(A) = .06$, $B = Mother$, $P(B) = .05$ +$A = Father$, $P(A) = .10$, $B = Mother$, $P(B) = .09$ $P(A\cup B) = .15$, *** .explanation -$P(A\cup B) = P(A) + P(B) - 2 P(AB)$ thus -$$.15 = .06 + .05 - 2 P(AB)$$ +$P(A\cup B) = P(A) + P(B) - P(AB)$ thus +$$.15 = .10 + .09 - P(AB)$$ ```{r} -(0.15 - .06 - .05) / 2 +.10 + .09 - .15 ``` --- &radio diff --git a/06_StatisticalInference/homework/hw2.Rmd b/06_StatisticalInference/homework/hw2.Rmd index 3a568425c..b38eab299 100644 --- a/06_StatisticalInference/homework/hw2.Rmd +++ b/06_StatisticalInference/homework/hw2.Rmd @@ -157,10 +157,10 @@ Let $p=.5$ and $X$ be binomial *** .explanation -`r round(pbinom(4, prob = .5, size = 6, lower.tail = TRUE) * 100, 1)` +`r round(pbinom(4, prob = .5, size = 6, lower.tail = FALSE) * 100, 1)` ```{r} -round(pbinom(4, prob = .5, size = 6, lower.tail = TRUE) * 100, 1) +round(pbinom(4, prob = .5, size = 6, lower.tail = FALSE) * 100, 1) ``` --- &multitext @@ -210,9 +210,9 @@ If you roll ten standard dice, take their average, then repeat this process over $$Var(\bar X) = \sigma^2 /n$$ *** .explanation -The answer will be `r round( mean(1 : 6 - 3.5) ^2 / 100, 3)` -since the variance of the sampling distribution of the mean is $\sigma^2/12$ -and the variance of a die roll is +The answer will be `r round( mean( (1 : 6 - 3.5) ^2) / 10, 3)` +since the variance of the sampling distribution of the mean is $\sigma^2/10$ +where $\sigma^2$ is the variance of a single die roll, which is ```{r} mean((1 : 6 - 3.5)^2)