Find the cardinality of the following set. A = { 12 , 14 , 16 , 18 , 20 }

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

Westkost [7]

Answer:

(a) The value of k 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 y.

Step-by-step explanation:

The random variable Y 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 k.

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

Thus, the value of k 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:

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

Check condition 1:

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

Condition 1 is fulfilled.

Check condition 2:

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

Condition 2 is not satisfied.

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

7 0

3 years ago

Dominic and Terrell plan to start their weekend backpacking trip on Friday at 4:20 P.M, and return home on Sunday at 5:40 A.M. H

Aleonysh [2.5K]

I think the answer is 4.20 hours and minutes planning the last road trip .

6 0

3 years ago

Jaime is 2 years older than Alejandra. In 5 years the sum of their ages will be 80. How old is Jaime now?

Dima020 [189]

Answer:

20 age This is right answer

7 0

3 years ago

segment CD has endpoints at C(0, 3) and D(0, 8). If the segment is dilated by a factor of 2 about point C, what is the length of

MatroZZZ [7]

The length of the image of the segment CD is 10 units if the segment CD has endpoints at C(0, 3) and D(0, 8).

<h3>What is a distance formula?</h3>

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

$\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have two points C(0, 3) and D(0, 8)

The distance between these two points:

d = √(8-3)²

d = 5 units

The length of the image of segments CD = dilation factor×length of CD

= 2×5

= 10 units

Thus, the length of the image of the segment CD is 10 units if the segment CD has endpoints at C(0, 3) and D(0, 8).

Learn more about the distance formula here:

brainly.com/question/18296211

#SPJ1

7 0

2 years ago

What is the gcf of 36 and 63?

Andrew [12]

The GCF would be 9.

You would first find the prime 36=2*2*3*3

Then do the same with 63. 63=3*3*7

So to find the GCF you would multiply the prime factors that are the same with 36 and 63. So you would multiply 3*3 which would give you 9.

GCF=9

8 0

3 years ago