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Karo-lina-s [1.5K]
3 years ago
8

Show that the following rational number by expressing it as a ratio quotient of two integers 0.9

Mathematics
1 answer:
kipiarov [429]3 years ago
7 0
A rational number can be expressed in the form a/b, where a and b are other integers.  To satisfy this definition, 0.9 can be written as 9/10, 18/20, 90/100, etc.
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Let X be a Bernoulli rv with pmf as in Example 3.18. a. Compute E(X2 ). b. Show that V(X) 5 p(1 2 p). c. Compute E(X79).
spayn [35]

The Bernoulli distribution is a distribution whose random variable can  only take 0 or 1

  • The value of E(x2) is p
  • The value of V(x) is p(1 - p)
  • The value of E(x79) is p

<h3>How to compute E(x2)</h3>

The distribution is given as:

p(0) = 1 - p

p(1) = p

The expected value of x2, E(x2) is calculated as:

E(x^2) = \sum x^2 * P(x)

So, we have:

E(x^2) = 0^2 * (1- p) + 1^2 * p

Evaluate the exponents

E(x^2) = 0 * (1- p) + 1 * p

Multiply

E(x^2) = 0 +p

Add

E(x^2) = p

Hence, the value of E(x2) is p

<h3>How to compute V(x)</h3>

This is calculated as:

V(x) = E(x^2) - (E(x))^2

Start by calculating E(x) using:

E(x) = \sum x * P(x)

So, we have:

E(x) = 0 * (1- p) + 1 * p

E(x) = p

Recall that:

V(x) = E(x^2) - (E(x))^2

So, we have:

V(x) = p - p^2

Factor out p

V(x) = p(1 - p)

Hence, the value of V(x) is p(1 - p)

<h3>How to compute E(x79)</h3>

The expected value of x79, E(x79) is calculated as:

E(x^{79}) = \sum x^{79} * P(x)

So, we have:

E(x^{79}) = 0^{79} * (1- p) + 1^{79} * p

Evaluate the exponents

E(x^{79}) = 0 * (1- p) + 1 * p

Multiply

E(x^{79}) = 0 + p

Add

E(x^{79}) = p

Hence, the value of E(x79) is p

Read more about probability distribution at:

brainly.com/question/15246027

5 0
2 years ago
Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS,
MariettaO [177]

Answer:

ΔPTS≅ΔRTA by AAS axiom of congruency

Step-by-step explanation:

Consider ΔPQA and ΔRQS

∠PQA=∠RQS     (Vertically Opposite Angles)

∠QAP=∠QSR     (Complementary of two equal angles, ∠RAT and∠PST)

Due to angle sum property of a triangle, we come to the conclusion that

∠APQ=∠SRQ

Consider ΔPTS and ΔRTA

TA=TS  (Given)

∠RAT=∠PST(Given)

∠APQ=∠SRQ (Proved above)

Therefore, ΔPTS≅ΔRTA by AAS axiom of congruency.

8 0
3 years ago
A circle has a radius of 6 feet. Calculate the area of the<br> sector formed by a central 30° angle
Tems11 [23]

Answer:

The area of the sector is 9.43 ft^2

Step-by-step explanation:

Here, we want to find the area of the sector with a central angle of 30 degrees

To do this, we use the formula below;

Area of sector = theta/360 * pi * r^2

theta = central angle = 30 degrees

r = radius = 6 ft

Thus, we have it that;

Area of sector = 30/360 * pi * 6^2

= 30/10 * pi = 3 * 3.142 = 9.43 ft^2

6 0
3 years ago
Consider the relationship below, given . Which of the following best explains how this relationship and the value of sin can be
vova2212 [387]

Answer:

The values of sin θ and cos θ represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos θ finds the unknown leg, and then all other trigonometric values can be found.

5 0
3 years ago
Read 2 more answers
What is the slope of the line graphed in the coordinate grid?
zvonat [6]

Answer:

3/4

Step-by-step explanation:

I drew a slope triangle and found the slope by finding the distance between two points on the line.

vertical distance/horizontal distance

Hope this helped!

5 0
3 years ago
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