Practice Math Statistics Problems and Master the Concepts

Let X and Y be independent, continuous random variables with the same maginal probability density function, defined as
$f_{X} (t) = f_{Y} (t) = {\begin{cases} \frac{2}{t^{2}}, t > 2 \\ 0, o t h e r w i s e \end{cases}$
(a)What is the joint probability density function f(x,y)?
(b)Find the probability density of W=XY. Hind: Determine the cdf of Z.

naivlingr 2021-06-06

Let p be the population proportion for the situation. (a) Find point estimates of p and q, (b) construct 90% and 95% confidence intervals for p, and (c) interpret the results of part (b) and compare the widths of the confidence intervals. In a survey of 1003 U.S. adults, 451 believe that for a person to be considered truly American, it is very important that he or she share American customs and traditions.

bobbie71G 2021-06-05

The joint density function of two continuous random variables X and Y is:
$f (x, y) = f (x, y) = {\begin{cases} c x^{2} e^{\frac{- y}{3}} & 1 < x < 6, 2 < y < 4 = 0 \\ 0 & o t h e r w i s e \end{cases}$
Draw the integration boundaries and write the integration only for $P (X + Y \leq 6)$

Nann 2021-06-05

Two random variables X and Y with joint density function given by:
$f (x, y) = {\begin{cases} \frac{1}{3} (2 x + 4 y) & 0 \leq x, \leq 1 \\ 0 & e l s e w h e r e \end{cases}$
Find the marginal density of X.

Wribreeminsl 2021-06-05

For each pair of variables, indicate whether a two-way table would be appropriate for summarizing the relationship. In each case, briefly explain why or why not. Satisfaction with quality of local K through 12 schools (satisfied or not satisfied) and political party (Republican, Democrat, etc.). Height (centimeters) and foot length (centimeters).

Annette Arroyo 2021-06-04

Use the one-standard-deviation $x^{2}$ -test and the one-standard-deviation $x^{2}$ -interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. $s = 6$ and $n = 26$
a. $H_{0} : σ = 5, H_{a} : σ > 5, α = 0.01$ .
b. 98% confidence interval.

vazelinahS 2021-06-04

Let $X_{1}, X_{2}, . . ., X_{n}$ be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables.
Find n such that $P r (X > 2000) \geq 0.95$ .

Jerold 2021-06-04

Find the correlation coefficient between the tandom variables X and Y if the covariance of X and Y is 0.9 and variances of the random variables X and Y are 4 and 9, respectively
1)0.142
2)0.133
3)0.150
4)0.125

FizeauV 2021-06-04

Consider the two samples of data from the McKenzie School. The numbers represent the time in seconds that it took each child to cover a distance of 50 meters. Girls’ Times: 8.3, 8.6, 9.5, 9.5, 9.6, 9.8, 9.9, 9.9, 10.0, 10.0, 10.0, 10.1, 10.3, 10.5 Boys’ Times: 7.9, 8.0, 8.2, 8.2, 8.4, 8.6, 8.8, 9.1, 9.3, 9.5, 9.8, 9.8, 10.0, 10.1, 10.3. Based on the sample means, do you conclude that the distributions of times from the boys’ population and girls’ population are different? Explain.

Rui Baldwin 2021-06-03

Find the expected values and variances of the exponential random variables with the density functions given below
$\frac{1}{4} e^{- \frac{x}{4}}$

Bevan Mcdonald 2021-06-03

Assume that X and Y are jointly continuous random variables with joint probability density function given by
$f (x, y) = {\begin{cases} \frac{1}{36} (3 x - x y + 4 y) i f 0 < x < 2 a n d 1 < y < 3 \\ 0 o t h r e w i s e \end{cases}$
Find the marginal density functions for X and Y .

Jerold 2021-06-03

Consider two continuous random variables X and Y with joint density function
$f (x, y) = {\begin{cases} x + y o \leq x \leq 1, 0 \leq y \leq 1 \\ 0 o t h e r w i s e \end{cases}$
$P (X > 0.8, Y > 0.8)$ is?

Albarellak 2021-06-03

Compute the distribution of $X + Y$ in the following cases:
X and Y are independent Poisson random variables with means respective $λ_{1} a n d λ_{2}$ .

a2linetagadaW 2021-06-03

The American Journal of Political Science (Apr. 2014) published a study on a woman's impact in mixed-gender deliberating groups. The researchers randomly assigned subjects to one of several 5-member decision-making groups. The groups' gender composition varied as follows: 0 females, 1 female, 2 females, 3 females, 4 females, or 5 females. Each group was the n randomly assigned to utilize one of two types of decision rules: unanimous or majority rule. Ten groups were created for each of the $6 \times 2 = 12$ combinations of gender composition and decision rule. One variable of interest, measured for each group, was the number of words spoken by women on a certain topic per 1,000 total words spoken during the deliberations. a. Why is this experiment considered a designed study? b. Identify the experimental unit and dependent variable in this study. c. Identify the factors and treatments for this study.

emancipezN 2021-06-03

Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. Gasoline: number of miles you drove since filling up, gallons remaining in your tank

Jason Farmer 2021-06-02

True or false?
a. The center of a 95% confidence interval for the population mean is a random variable.
b. A 95% confidence interval for μμ contains the sample mean with probability .95.
c. A 95% confidence interval contains 95% of the population.
d. Out of one hundred 95% confidence intervals for μμ, 95 will contain μμ.

Tammy Todd 2021-06-02

Let p be the population proportion for the situation. (a) Find point estimates of p and q, (b) construct 90% and 95% confidence intervals for p, and (c) interpret the results of part (b) and compare the widths of the confidence intervals. In a survey of 2223 U.S. adults, 1334 say an occupation as an athlete is prestigious.

banganX 2021-06-02

The joint density of the random variables X and Y is given by
$f (x, y) = {\begin{cases} 8 x y & 0 \leq x \leq 1, 0 \leq y \leq x \\ 0 & o t h e r w i s e \end{cases}$
Find the marginal density of X

Wierzycaz 2021-06-02

Suppose that X and Y are continuous random variables with joint pdf $f (x, y) = e^{- (x + y)} 0$ and zero otherwise.
Find $P (X > Y)$

Rivka Thorpe 2021-06-01

The continuous random variables X and Y are statistically independent and have marginal density functions $f_{X} (x) = 2 x, 0 \leq x \leq 1, f_{Y} (y) = \frac{1}{y^{2}}, y \geq 1$ .
Calculate the probability $P (X \leq 0.5, Y \leq 2) =$ ?

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