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
aniked [119]
2 years ago
12

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature

of the project) in applying for a building permit. Let Y = the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y; that is, p(y) = ky for y = 1,..., 5.
(a) What is the value of k?
(b) What is the probability that at most three forms are required?
(c) What is the probability that between two and four forms (inclusive) are required?
(d) Could p(y) = y^2/50 for y = 1,..., 5 be the pdf (pmf) of Y?
Mathematics
1 answer:
Westkost [7]2 years ago
7 0

Answer:

(a) The value of <em>k</em> is \frac{1}{15}.

(b) The probability that at most three forms are required is 0.40.

(c) The probability that between two and four forms (inclusive) are required is 0.60.

(d)  P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5 is not the pmf of <em>y</em>.

Step-by-step explanation:

The random variable <em>Y</em> is defined as the number of forms required of the next applicant.

The probability mass function is defined as:

P(y) = \left \{ {{ky};\ for \ y=1,2,...5 \atop {0};\ otherwise} \right

(a)

The sum of all probabilities of an event is 1.

Use this law to compute the value of <em>k</em>.

\sum P(y) = 1\\k+2k+3k+4k+5k=1\\15k=1\\k=\frac{1}{15}

Thus, the value of <em>k</em> is \frac{1}{15}.

(b)

Compute the value of P (Y ≤ 3) as follows:

P(Y\leq 3)=P(Y=1)+P(Y=2)+P(Y=3)\\=\frac{1}{15}+\frac{2}{15}+ \frac{3}{15}\\=\frac{1+2+3}{15}\\ =\frac{6}{15} \\=0.40

Thus, the probability that at most three forms are required is 0.40.

(c)

Compute the value of P (2 ≤ Y ≤ 4) as follows:

P(2\leq Y\leq 4)=P(Y=2)+P(Y=3)+P(Y=4)\\=\frac{2}{15}+\frac{3}{15}+\frac{4}{15}\\   =\frac{2+3+4}{15}\\ =\frac{9}{15} \\=0.60

Thus, the probability that between two and four forms (inclusive) are required is 0.60.

(d)

Now, for P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5 to be the pmf of Y it has to satisfy the conditions:

  1. P(y)=\frac{y^{2}}{50}>0;\ for\ all\ values\ of\ y \\
  2. \sum P(y)=1

<u>Check condition 1:</u>

y=1:\ P(y)=\frac{y^{2}}{50}=\frac{1}{50}=0.02>0\\y=2:\ P(y)=\frac{y^{2}}{50}=\frac{4}{50}=0.08>0 \\y=3:\ P(y)=\frac{y^{2}}{50}=\frac{9}{50}=0.18>0\\y=4:\ P(y)=\frac{y^{2}}{50}=\frac{16}{50}=0.32>0 \\y=5:\ P(y)=\frac{y^{2}}{50}=\frac{25}{50}=0.50>0

Condition 1 is fulfilled.

<u>Check condition 2:</u>

\sum P(y)=0.02+0.08+0.18+0.32+0.50=1.1>1

Condition 2 is not satisfied.

Thus, P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5 is not the pmf of <em>y</em>.

You might be interested in
Ari and Greg share a 12-ounce bucket of clay. By the end of the week, Ari has used 1 6 of the bucket, and Greg has used 2 3 of t
kotegsom [21]

Answer:

2 ounces of clay is left in the bucket

Step-by-step explanation:

Total amount of clay in the bucket = 12 ounce

Ari used 1/6th of the clay in the bucket and Greg used 2/3 of the clay in the bucket

Hence, the remaining clay in the bucket

12 - 1/6 *12 - 2/3 * 12

12 - 2-8

2

3 0
2 years ago
Which of the following is a true equation?<br> k=y/x<br> k= x/y<br> x= y/k
faust18 [17]

Answer:

Step-by-step explanation:

Your question is not complete.

According to what do we validate with the equation.

add more info in the question because all of them can be true without any condition given or validation.

7 0
3 years ago
What is the standard deviation of the following data set rounded to the nearest tenth
photoshop1234 [79]

Answer:

73nejejejeex

Step-by-step explanation:

5 0
2 years ago
A regular heptagon is shown below. What is the value of x?
Margaret [11]

Answer:

108+x=180

X=180-108

X=72

7 0
2 years ago
Simplify the expression: the square root of -13 times the square root of -26 calculator
Rasek [7]
Sqrt -13  = sqrt13 i
sqrt  -26  =  sqrt2 * sqrt13i 

sqrt-13 * sqrt -26  = sqrt2 * 13*  i^2  = -13 sqrt2 (because i^2 = -1)

answer is -13 sqrt2
6 0
3 years ago
Other questions:
  • PLEASE ANSWER ASAP!!!
    6·1 answer
  • A grocer has two kinds of candies: one sells for 90 cents per pound and the other sells for 40 cents per pound. How many pounds
    14·1 answer
  • 1
    12·1 answer
  • Use the drawing tool(s) to form the correct answer on the provided graph.
    6·1 answer
  • Evaluate using the order of operation 3/4+5/6÷2/3
    8·1 answer
  • Write in scienctific notation<br> .00000758
    13·2 answers
  • Find the volume of the given rectangular prism.
    14·1 answer
  • I need help with this math problem not sure what to do?​
    11·1 answer
  • A suit originally costing $240 is on sale for 25% off the original price. Sales tax is 7.5%. What is the final cost of the suit?
    9·2 answers
  • PLEASE HELP ME ON THIS ONE
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!