Hows the weather today..?

(4.1.4) Let X and Y be Bernoulli random variables. Let Z = X + Y. a. Show that if X and Y cannot both be equal to 1, then Z is a

Fynjy0 [20]

Step-by-step explanation:

Given that,

a)

X ~ Bernoulli $(p_x)$ and Y ~ Bernoulli $(y_x)$

X + Y = Z

The possible value for Z are Z = 0 when X = 0 and Y = 0

and Z = 1 when X = 0 and Y = 1 or when X = 1 and Y = 0

If X and Y can not be both equal to 1 , then the probability mass function of the random variable Z takes on the value of 0 for any value of Z other than 0 and 1,

Therefore Z is a Bernoulli random variable

b)

If X and Y can not be both equal to 1

then,

$p_z = P(X=1$ or $Y=1)\\$

$p_z = P(X=1)+P(Y=1)-P(=1$ and $Y =1)$

$p_z = P(x=1)+P(Y=1)\\\\p_z=p_x+p_y$

c)

If both X = 1 and Y = 1 then Z = 2

The possible values of the random variable Z are 0, 1 and 2.

since a Bernoulli variable should be take on only values 0 and 1 the random variable Z does not have Bernoulli distribution

7 0

3 years ago

What’s 5(x-4)+2 as a verbal expression?

sesenic [268]

The verbal expression for the mathematical expression 5(x - 4) + 2 is the number 5 times the difference between an unknown x and the number 4 and plus 2.

<h3>What is an expression?</h3>

It is defined as the combination of constants and variables with mathematical operators.

It is given that a mathematical expression as below:

= 5(x - 4) + 2

Here x is the unknown number

The number

Number 5 times the difference between an unknown x and number 4 and plus 2

Thus, the verbal expression for the mathematical expression 5(x - 4) + 2 is number 5 times the difference between an unknown x and number 4 and plus 2.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ1

7 0

1 year ago

Solve for x in the equation 3 x squared minus 18 x + 5 = 47.

ryzh [129]

Answer:

x= 3 + $\sqrt{23}$ , 3 - $\sqrt{23}$

Step-by-step explanation:

You use the quadratic formula to get x= $\frac{18+6\sqrt{23} }{6} ,\frac{18-6\sqrt{23} }{6}$

Then you simplify and get the answers x= 3 + $\sqrt{23}$ , 3 - $\sqrt{23}$

6 0

3 years ago

Read 2 more answers

Ewen has 48 whistle tiles and 16 blue tiles the cost of each white tile was £2 and the cost of each blue tile was £4 Work out th

AnnZ [28]

Answer:

3:2

Step-by-step explanation:

Ewen has 48 white tiles and 16 blue tiles

The cost of each white tile was £2

The cost of each blue tile was £4

Therefore the total cost of 48 white tiles is

= 48×2

= £96

The total cost of 16 blue tiles is

= 16×4

= £64

The ratio of the total cost of the white tiles and blue tile can be calculated by dividing the cost of both tiles by their greatest common factor

The greatest common factor of £96 and £64 is 32

96/32 = 3

64/32= 2

Ratio= 3:2

Hence the ratio of the total cost of the white tiles to the blue tiles is 3:2

6 0

3 years ago

Factorize ху + 3x +3y + 18

noname [10]

Answer:

(x+6)(y+3)

Step-by-step explanation:

xy + 3x + 6y + 18
x(y + 3) + 6(y+3)
(x+6)(y+3)

3 0

2 years ago

Hows the weather today..?​

Hows the weather today..?