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aksik [14]
3 years ago
8

A box contains four bowling balls numbered 2, 4, 6, and 10 according to their weight. Two are drawn randomly without replacement

. Let the random variable M denote the max of the two numbers on the balls drawn. Calculate E(M) and Var(M). Hint: Start by specifying the joint distribution of the number on the balls.
Mathematics
1 answer:
Lilit [14]3 years ago
5 0

Answer:

E(M) = 23/3

Var(M) = 53/9.

Step-by-step explanation:

There are three possible values for M: 4, 6, and 10.

\begin{array}{|l|l|}\cline{1-2}\\[-1em]\text{Larger Number} & \text{Smaller Number}\\ \cline{1-2}\\[-1em]4 & 2 \\\cline{1-2}\\[-1em]6 & 2, ~4\\\cline{1-2}\\[-1em] 10 & 2, ~4, ~6\\\cline{1-2} \end{array}.

That's six unique combinations in total. If the balls are drawn randomly, the probability for getting each combination shall be equal. That is:

\begin{array}{|c|c|}\cline{1-2}\\[-1em]m & P(\text{M} = m)\\\cline{1-2}\\[-1em] 2 & 0\\\cline{1-2}\\[-1em] 4 & 1/6 \\\cline{1-2}\\[-1em] 6 & 2/6\\\cline{1-2}\\[-1em] 10 & 3/6\\\cline{1-2}\end{array}.

Consider the formula for the expected value of a discrete random variable:

\begin{aligned} E({\rm M})& = \sum{[m \cdot P(\mathrm{M} = m)]}\\ &= 4 \times \frac{1}{6} + 6\times \frac{2}{6} + 10 \times \frac{3}{6}\\ &= \frac{23}{3}\end{aligned}.

Formula for the variance of a discrete random variable (note that this formula can take many other forms):

\begin{aligned}Var(\mathrm{M}) &= \sum{[m^{2}\cdot P(\mathrm{M}= m)]} - \mu^{2}\\&= 4^{2}\times \frac{1}{6} + 6^{2} \times \frac{2}{6} + 10^{2} \times \frac{3}{6} - \left(\frac{23}{3}\right)^{2}\\&= \frac{53}{9}\end{aligned}.

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goblinko [34]

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<h3><u>Solution:</u></h3>

Given that to find sum of prime factors of 2014

Let us first find the prime factors of 2014

A prime number is a whole number greater than 1 whose only factors are 1 and itself

"Prime Factorization" is finding which prime numbers multiply together to make the original number.

<em><u>Prime factors of 2014:</u></em>

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Thus the prime factors of 2014 are 2, 19, 53

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Step-by-step explanation:

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An equation which can be used to solve the given system of equations is 3x⁵ - 5x³ + 2x² - 10x + 4 = 4x⁴ + 6x³ - 11.

<u>Given the following data:</u>

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A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneoulsy.

Equating the given equations, we have:

y = y

3x⁵ - 5x³ + 2x² - 10x + 4 = 4x⁴ + 6x³ - 11

3x⁵ - 5x³ + 2x² - 10x + 4 - (4x⁴ + 6x³ - 11) = 0

3x⁵ - 5x³ + 2x² - 10x + 4 - 4x⁴ - 6x³ + 11 = 0

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Read more on equations here: brainly.com/question/13170908

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