The table shows the number of feathers Patsy the Peacock sold at each of the 888 festivals this year.

An urn contains three white balls and two red balls. The balls are drawn from the urn, oneat a time without replacement, until a

Tpy6a [65]

Answer:

p ( X = 1 ) = 0.6 , p ( X = 2 ) = 0.3 , p ( X = 3 ) = 0.1

Verified

E ( X ) = 1.5

Step-by-step explanation:

Solution:-

- An urn contains the following colored balls:

Color Number of balls

White 3

Red 2

- A ball is drawn from urn without replacement until a white ball is drawn for the first time.

- We will construct cases to determine the distribution of the random-variable X: The number of trials it takes to get the first white ball.

- We have three following case:

1) White ball is drawn on the first attempt ( X = 1 ). The probability of drawing a white ball in the first trial would be:

p ( X = 1 ) = ( Number of white balls ) / ( Total number of ball )

p ( X = 1 ) = ( 3 ) / ( 5 )

2) A red ball is drawn on the first draw and a white ball is drawn on the second trial ( X = 2 ). The probability of drawing a red ball first would be:

p ( Red on first trial ) = ( Number of red balls ) / ( Total number of balls )

p ( Red on first trial ) = ( 2 ) / ( 5 )

- Then draw a white ball from a total of 4 balls left in the urn ( remember without replacement ).

p ( White on second trial ) = ( Number of white balls ) / ( number of balls left )

p ( White on second trial ) = ( 3 ) / ( 4 )

- Then to draw red on first trial and white ball on second trial we can express:

p ( X = 2 ) = p ( Red on first trial ) * p ( White on second trial )

p ( X = 2 ) = ( 2 / 5 ) * ( 3 / 4 )

p ( X = 2 ) = ( 3 / 10 )

3) A red ball is drawn on the first draw and second draw and then a white ball is drawn on the third trial ( X = 3 ). The probability of drawing a red ball first would be ( 2 / 5 ). Then we are left with 4 balls in the urn, we again draw a red ball:

p ( Red on second trial ) = ( Number of red balls ) / ( number of balls left )

p ( Red on second trial ) = ( 1 ) / ( 4 )

- Then draw a white ball from a total of 3 balls left in the urn ( remember without replacement ).

p ( White on 3rd trial ) = ( Number of white balls ) / ( number of balls left )

p ( White on 3rd trial ) = ( 3 ) / ( 3 ) = 1

- Then to draw red on first two trials and white ball on third trial we can express:

p ( X = 3 ) = p ( Red on 1st trial )*p ( Red on 2nd trial )*p ( White on 3rd trial )

p ( X = 3 ) = ( 2 / 5 ) * ( 1 / 4 ) * 1

p ( X = 3 ) = ( 1 / 10 )

- The probability distribution of X is as follows:

X 1 2 3

p ( X ) 0.6 0.3 0.1

- To verify the above the distribution. We will sum all the probabilities for all outcomes ( X = 1 , 2 , 3 ) must be equal to 1.

∑ p ( Xi ) = 0.6 + 0.3 + 0.1

= 1 ( proven it is indeed a pmf )

- The expected value E ( X ) of the distribution i.e the expected number of trials until we draw a white ball for the first time:

E ( X ) = ∑ [ p ( Xi ) * Xi ]

E ( X ) = ( 1 ) * ( 0.6 ) + ( 2 ) * ( 0.3 ) + ( 3 ) * ( 0.1 )

E ( X ) = 0.6 + 0.6 + 0.3

E ( X ) = 1.5 trials until first white ball is drawn.

8 0

4 years ago

At what values of x does the graph of f(x)= sin x intersect the x-axis?

aalyn [17]

D) not fully sure thoe

8 0

3 years ago

Read 2 more answers

Mckinney donated 9 soda bottles to the after

Papessa [141]

Answer:

33%

Step-by-step explanation:

9 - 6 = 3

3 / 9 = 0.33

0.33 x 100 = 33%

Amount of what you have divided by the total amount of something, times by 100 gives you the percentage

4 0

3 years ago

Read 2 more answers

Question 3

34kurt

Answer:

The distance from point A to the line of reflection is the same as the distance from point AGH to the line of reflection. This means that the line of reflection bisects .

1) 4 2 2

2) 5.77 2.89 2.89

3) 7.9 3.95 3.95

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A random sample of ten 2011 sports cars is taken and their city mileage is recorded. The results are as follows: 20 21 25 21 21

serious [3.7K]

Answer:

$ME = 1.833 * \frac{4.367}{\sqrt{10}}= 2.531$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=24.8$

The sample deviation calculated $s=4.367$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=10-1=9$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,9)".And we see that $t_{\alpha/2}=1.833$

And the margin of error would be given by:

$ME = 1.833 * \frac{4.367}{\sqrt{10}}= 2.531$

5 0

4 years ago