Mathematics, 30.01.2020 19:00 redraider4915

Which of the following is not a valid probability distribution for a discrete random variable? check all that apply.

a. 1/5,1/10 ,1/10 ,1/10 ,1/5 ,1/10 ,1/10 , 1/10

b. 1/3,1/4 ,1/5 ,1/6

c. 1/2,1/4 ,1/8 ,1/16 ,1/32 ,1/64 ,1/128 ,1/128

d. -1/2, -1/3, -1/4, -1/5, 137/60

e. 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

Answers: 3

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Answer from: Coledyer

Option B and D are correct.

Step-by-step explanation:

We know that Sum of the probability distribution of a discrete random variable is equal to 1.

using this result we check which is not valid probability distribution.

Option A).

Sum of Probability Distribution

$=\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{2+1+1+1+2+1+1+1}{10}=\frac{10}{10}=1$

So, This is valid Probability distribution.

Option B).

Sum of Probability Distribution

$=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{20+15+12+10+}{60}=\frac{57}{10}\neq1$

So, This is not a valid Probability distribution.

Option C).

Sum of Probability Distribution

$=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{128}=\frac{64+32+16+8+4+2+1+1}{128}=\frac{128}{128}=1$

So, This is valid Probability distribution.

Option D).

Given Probability Distribution has negative probability which is not possible.

So, This is not a valid Probability distribution.

Option E).

Sum of Probability Distribution

$=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1+1+1+1+1+1}{6}=\frac{6}{6}=1$

So, This is valid Probability distribution.

Therefore, Option B and D are correct.

Answer from: Quest

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that runner b is moving at a slower rate."

Answer from: Quest

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1 1

1 2

1 3

1 4

2 1

2 2

2 3

2 4 = not 1, and 4

3 1

3 2

3 3

3 4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

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