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2 years ago

Suppose that in a casino game the payout is a random variable X . If X is positive, you gain money, if negative, you lose.

Mathematics

1 answer:

Vanyuwa [196]2 years ago

8 0

Answer:

the conditional probability that X = 1 , X = 2 and X = 3 is 0.7333 (73.33%) , 0.25 (25%) and 0.0167 (1.67%) respectively

Step-by-step explanation:

a player wins money when i>0 then defining event W= gain money , then

P(W) = p(i>0) = p(1)+p(2)+p(3)

then the conditional probability can be calculated through the theorem of Bayes

P(X=1/W)= P(X=1 ∩ W)/P(W)

where

P(X=1 ∩ W)= probability that the payout is 1 and earns money

P(X=1 / W)= probability that the payout is 1 given money was earned

then

P(X=1/W)= P(X=1 ∩ W)/P(W) = P(X=1) / P(W) = p(1) /[p(1)+p(2)+p(3)] = 11/40 /(11/40+3/32+1/160 ) = 0.7333 (73.33%)

similarly

P(X=2/W)=p(2) /[p(1)+p(2)+p(3)] = 3/32 /(11/40+3/32+1/160 ) = 0.25 (25%)

P(X=3/W)=p(2) /[p(1)+p(2)+p(3)] = 1/160 /(11/40+3/32+1/160 ) = 0.0167 (1.67%)

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Below are boxplots that summarize the weights (in pounds) of large samples from two breeds of dog: the Anatolian Shepherd and th

koban [17]

Answer:

(a) The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of both plots is also same that is 75 pounds.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively

(b) Any data point which is greater than 155 or smaller than 80 will be considered an outlier.

Step-by-step explanation:

A box plot is a graph which shows five statistical characteristics of a data set.

1. Maximum value

2. Minimum value

3. Median

4. Upper Interquartile

5. Lower interquartile

(a) Compare the distributions of weights for the two dog breeds

Please refer to the attached diagram of the question.

The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of Anatolian Shepherd is,

Range = Maximum value - Minimum value

Range = 175 - 100 = 75 pounds

The range of Black Russian Terrier is,

Range = Maximum value - Minimum value

Range = 155 - 80 = 75 pounds

Therefore, the range of both plots is also same that is 75 pounds.

A box-plot is considered to be normally distributed when the median is at the center of upper quartile and lower quartile.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively distributed.

(b) What weights would a Black Russian Terrier have to be to be considered an outlier?

An outlier is a data point in the data set that is very different from the other data points.

In this case, the maximum and minimum values in the Black Russian Terrier box-plot are

Maximum = 155

Minimum = 80

Therefore, any data point which is greater than 155 or smaller than 80 will be considered an outlier.

5 0

2 years ago

A textbook has 500 pages on which typographical errors could occur. Suppose that there are exactly 10 such errors randomly locat

DiKsa [7]

Answer:

The probability of a selection of 50 pages will contain no errors is 0.368

The probability that the selection of the random pages will contain at least two errors is 0.2644

Step-by-step explanation:

From the information given:

Let q represent the no of typographical errors.

Suppose that there are exactly 10 such errors randomly located on a textbook of 500 pages. Let $\mu$ be the random variable that follows a Poisson distribution, then mean $\mu = \dfrac{10}{500}= 0.02$

and the mean that the random selection of 50 pages will contain no error is $\lambda = 50 \times 0.02 =1$

∴

$Pr(q= 0) = \dfrac{e^{-1} (1)^0}{0!}$

Pr(q =0) = 0.368

The probability of a selection of 50 pages will contain no errors is 0.368

The probability that 50 randomly page contains at least 2 errors is computed as follows:

P(X ≥ 2) = 1 - P( X < 2)

P(X ≥ 2) = 1 - [ P(X = 0) + P (X =1 )] since it is less than 2

$P(X \geq 2) = 1 - [ \dfrac{e^{-1} 1^0}{0!} +\dfrac{e^{-1} 1^1}{1!} ]$

$P(X \geq 2) = 1 - [0.3678 +0.3678]$

$P(X \geq 2) = 1 -0.7356$

P(X ≥ 2) = 0.2644

The probability that the selection of the random pages will contain at least two errors is 0.2644

6 0

2 years ago

Select the term that does NOT describe the triangle. Select all that apply

emmainna [20.7K]

Answer:

this isnt an isosceles.

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2 years ago

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Luka's weekly earnings of $475 are increased by 6% calculate his new weekly earnings

KengaRu [80]

He earns 28.5. (475•0.06)

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2 years ago

Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance fro the same section of the race is disp

sergey [27]

Step-by-step explanation:

Ryan had a head start of 10 meters.

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2 years ago

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