1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}.

You might be interested in
Write a word problem for x/2+4=12
dezoksy [38]

Answer:

Four more than half a number is twelve

Step-by-step explanation:

Four more than half a number is twelve

5 0
3 years ago
Find the percent increase. Round to the nearest percent.
kakasveta [241]

Answer:

80%

Step-by-step explanation:

from $25 to $45

$45/$25 = 1.8

$25 x 1.8 = $45

therefore, the increase is 80%

8 0
3 years ago
Due to concerns about the underinflation of footballs, the National Football League (NFL) created a series of standards that mus
marshall27 [118]

Answer: 13.5/12.5

Step-by-step explanation:

6 0
3 years ago
Hey answer equation please thanks
Ainat [17]

Answer:

30 y

Step-by-step explanation:

We need to multiply 5 by 4y and 5 by 2 y

20y + 10y = 30y

6 0
3 years ago
Read 2 more answers
Polygon ABCD will be dilated by a scale factor of 2.2 with the origin as the center of dilation, resulting in the image A′B′C′D′
Citrus2011 [14]

m = undefined, C′D′ = 13.2 units

4 0
3 years ago
Other questions:
  • Evaluate tan (cos^ -1 (- 15/17 )
    7·2 answers
  • Two numbers are said to be 'relatively prime' if their greatest common factor is 1. How many integers greater than 10 and less t
    9·1 answer
  • What is the mean of the following set of numbers?
    5·2 answers
  • Factor x squared + 15x -54
    12·2 answers
  • 100000000000 to the 10th power
    12·1 answer
  • Which expression is equivalent to -42 x -1.5
    9·2 answers
  • Explain how you know if an ordered pair is a solution to an equation or not.
    15·1 answer
  • Megan paid $2.52 in sales tax on an item that cost $36.00 before tax. At that rate, how much would she pay in sales tax for an i
    12·1 answer
  • Plz help i need to do number 12 i need the area and perimeter make sure you round to the nearest whole number
    11·2 answers
  • PLS HELP I HAVE LIMITED TIME PLEASE GUYS
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!