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
The month of the year is December. What is the type of data is December?
scoundrel [369]

Data that is collected can be either categorical or numerical data.Categorical variables represent types of data which may be divided into groups.

December is the twelfth and last month of the year .The word December is a  categorical discrete data which is also known as qualitative, because it is a name instead of a number.Among the options given December is a month of a year.

The month of the year is December is a categorical data .

3 0
3 years ago
Read 2 more answers
Subtract. 0.63–(–9.85)<br> a. –10.48<br> b. –9.22<br> c. 9.22<br> d. 10.48
zaharov [31]
Negative times negative = positive.

=0.63−(−9.85)
=0.63+9.85
=10.48

D) is the answer.
5 0
3 years ago
Read 2 more answers
Answer ASAP
LiRa [457]

Answer:

x = 15°

Step-by-step explanation:

Complementary angles are two angles whose sum = 90°

∠A + ∠B = 90°

3x + 45 = 90

3x = 45

x = 45/3

x = 15°

8 0
2 years ago
What are the values of x and y​
andrey2020 [161]
X is 35 degrees and Y is 70 degrees
3 0
3 years ago
Which expression is the radical form of m to the power of -0.3333
Evgen [1.6K]

Answer:

A1/ ∛m

Step-by-step explanation:

m ^ (-1/3)

this is m to the cubed root in the denominator

1/ ∛m

8 0
3 years ago
Other questions:
  • Terry has a box that originally held 64 crayons. She is missing 25% of the crayons. How many crayons are missing?
    13·2 answers
  • Can someone help me please
    11·1 answer
  • What are all the exact solutions of -3tan^2x+1=0? Give your answers in radians.
    15·1 answer
  • Recently, frogs have been disappearing from the wild due to a contagious fungus. To monitor the current population in a certain
    14·2 answers
  • Once you have a single variable isolated in one of the two equations in a system, the second step of using substitution to solve
    9·2 answers
  • Solve the Following Equation................<br> 15(x+4)=-2
    5·1 answer
  • You are looking at the top of a building and thinking it would be great to make a zipline from the top to your current location.
    13·2 answers
  • What’s the equation?
    5·2 answers
  • What is 508.93 rounded to the nearest tenth
    13·2 answers
  • Find the sum of 5x3 3x²+5 and -2x²+6x²5
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!