Random Variable Problems & Solutions

How many different 10 letter words (real or imaginary) can be formed from the following letters
H,T,G,B,X,X,T,L,N,J.

Marisa Singleton 2023-03-24

For the 1s orbital of the Hydrogen atom, the radial wave function is given as: $R (r) = \frac{1}{\sqrt{π}} (\frac{1}{a_{O}})^{\frac{3}{2}} e^{\frac{- r}{a_{O}}}$ (Where $a_{O} = 0.529$ ∘A)
The ratio of radial probability density of finding an electron at $r = a_{O}$ to the radial probability density of finding an electron at the nucleus is given as ( $x . e^{- y}$ ). Calculate the value of (x+y).

villain hero2023-01-11

A student is asked to pick marbles from a bag that contains 18 marbles. 8 marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of red color?

Ada Lloyd 2022-11-27

When Sam goes to a restaurant, he always tips the sener $2 plus 10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution

Sagar Yadav2022-11-26

A customer organization that evaluates new automobiles customarily reports the
number of major defects in each car examined. Let ܺ denote the number of major
defects in a randomly selected car of a certain type. The cdf of ܺ is as follows:
= (ݔ)ܨ
ە
ۖ
ۖ
۔
ۖ
ۖ
ۓ
0 if ݔ > 0
0.06 if 0 ≤ ݔ > 1
0.19 if 1 ≤ ݔ > 2
0.39 if 2 ≤ ݔ > 3
0.67 if 3 ≤ ݔ > 4
0.92 if 4 ≤ ݔ > 5
0.97 if 5 ≤ ݔ > 6
1 if 6 ≤ ݔ
Calculate the following probabilities directly from the cdf.
a. ܲ(ܺ = 2)
b. ܲ(ܺ > 3)
c. ܲ(2 ≤ ܺ ≤ 5)
d. ܲ(2 < ܺ < 5)

Davirnoilc 2022-11-16

Classify each of the following random variables as discrete or continuous. Y = the number correct on a recent multiple-choice test for a randomly selected student in your class.

atgnybo4fq 2022-11-06

Find the distributions of the random variables that have each of the following moment generating functions:
$m (t) = e^{2 (e^{t} - 1)}$

Alberto Calhoun 2022-11-05

Suppose X and Y are two random variables such that $ρ (X, Y) = 1 / 2$ , Var X = 1, and Var Y = 2. Compute Var (X - 2Y).

Siemensueqw 2022-11-05

Determine the covariance and correlation for $X_{1}$ and $X_{2}$ in the joint distribution of the multinomial random variables $X_{1}, X_{2}$ and $X_{3}$ in with $p_{1} = p_{2} = p_{3} = \frac{1}{3}$ and n = 3. What can you conclude about the sign of the correlation between two random variables in a multinomial distribution?

Josiah Owens 2022-10-23

Suppose X and Y are two independent random variables such that $E X^{4} = 2, E Y^{2} = 1, E X^{2} = 1$ , and EY = 0. Compute $V a r (X^{2} Y)$

Tara Mayer 2022-10-21

Classify the following random variables as continuous or discrete: the number of hairs on a cat.

Tyson Atkins 2022-10-11

Classify the following random variables as continuous or discrete: the mark out of 50 for a geography test.

fofopausiomiava 2022-10-02

Classify the following random variables as continuous or discrete: the height of a sky-scraper.

Haiden Meyer 2022-10-02

Let $Z_{1}$ and $Z_{2}$ be independent standard normal random variables and $U_{1} = Z_{1}$ and $U_{2} = Z_{1} + Z_{2}$ . Are $U_{1}$ and $U_{2}$ independent? Why?

Bridger Holden 2022-10-02

Are all continuous random variables necessarily infinite? Explain.

Dana Russo 2022-09-29

Use the applet Gamma Probabilities and Quantiles to find the medians of gamma distributed random variables with parameters In all of these cases, the median exceeds the mean. How is that reflected in the shapes of the corresponding densities?

gsragator9 2022-09-29

For each of the following situations, would you expect the random variables X and Y to be independent? Explain your answers. X is the amount of rainfall today, and Y is the rainfall at the same location tomorrow.

lunja55 2022-09-25

Suppose that random variables X and Y vary in accordance with the joint pdf, $f_{X, Y} (x, y) = c (x + y), 0 < x < y < 1.$ . Find c.

Medenovgj 2022-09-25

Let X and Y be independent random variables each having a geometric density with parameter p. Find E[Y | X + Y = z] where z is a nonnegative integer.

memLosycecyjz 2022-09-25

Let $Y_{1}, Y_{2}, . . ., Y_{n}$ be independent, uniformly distributed random variables on the interval $[0, θ]$ . density function of $Y_{(n)}$

When you have an equation that deals with random variables, always start with an explanation related to some random variable examples. It is what the majority of skilled engineers do because it is the only way how one can avoid mistakes when working with statistical data. Even though this part of statistics and probability may seem overly complex, approach every random variable equation through the lens of probability as you seek answers to your questions. Compare provided solutions, see similarities, and you will achieve the most efficient solutions.

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