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3 years ago

6. A student driver travels at a speed of 3km/h for an hour and a half. What

Mathematics

1 answer:

castortr0y [4]3 years ago

5 0

Answer:

4.5 km

Step-by-step explanation:

3km times 1 = 3 and then 3km times .5 = 1.5

3+1.5= 4.5

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In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and

Leviafan [203]

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

Name the probabilities:

p₁ = 0.02, p₂ = 0.07, p₃ = 0.91

q₁ = 1-p₁ = 0.98 , q₂ = 1-p₂ = 0.93 , q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

The function will follow multinomial distribution:

$f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})$

Substitute the values and make a table.

TABLE IN ATTACHMENT

We calculate marginal distribution by:

$P (X=x)=$ <em>∑</em> $P(X=x,Y=y)$

$fx(x)$ can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

The mathematic expectation E is the sum of product of each possibility with its probabiity.

$E(X)=$ <em>∑ </em> $xP(X=x)$

Find E(X):

$E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)$

$E(X)=0.06$

Condition probability states:

$P(A|B)=\frac{P(A,B)}{P(B)}$

It can also be written as:

$f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}$

Where $f_x(1)\\$ = 0.057624

Calculate the quotient:

$Y|_{x=1}$ = 0 , $f_{Y|_X=1$ = 0.862245

$Y|_{x=1}$ = 1 , $f_{Y|_X=1$ = 0.132653

$Y|_{x=1}$ = 2 , $f_{Y|_X=1$ = 0.000510

$Y|_{x=1}$ = 3 , $f_{Y|_X=1$ = 0

Find the dependency:

$f_{XY}(y)=f_X(x)f_Y(y)$

We found that

$f_{Y|_X=1$ = 0.862245

Calculate $f_Y(1)$ from summing the column from the table

$f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141$

Which are not equal.

Conclusion:

X and Y are NOT Independent

7 0

4 years ago

What is <br> 12+5+3\2*10-5

fredd [130]

Answer:

787/32 or 24.59375

Step-by-step explanation:

I just looked it up lol

4 0

3 years ago

One angle of an isosceles triangle measures 62º. Which other angles could be in that

oee [108]

Answer:

62 and 56 or 59 and 59

Step-by-step explanation:

62, 62, 56

62, 59, 59

8 0

3 years ago

Read 2 more answers

River C is 300 Miles Longer than River D. If the sum of their lengths is 5,570 miles, what is the length of each river?

d1i1m1o1n [39]

$x-\ length\ of\ river\ D\\
x+300-\ length\ of\ river\ C\\\\
5570=x+x+300\\
5570=2x+300\ \ \ | subtract\ 300\\5270=2x\ \ \ | divide\ by\ 2\\x=2635\\\\
River\ C\ is\ 2935miles\ long\ and\ river\ D\ 2635\ miles\ long.$

6 0

3 years ago

OOOO

lbvjy [14]

Step-by-step explanation:

Given bi-quadratic equation is:

$x^4+95x^2 -500=0$

Substituting $x^2=a,$ given bi-quadratic equation reduces in the form of following quadratic equation:

$a^2 +95a -500=0\\$

Let us factorize the above quadratic equation:

$a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\$

Since square root of a negative number cannot be found, so:

$x \neq \pm \sqrt{-100}\\$

$CASE\: (2)\:\\When\: a =5 \implies x^2 =5\\\therefore x=\pm \sqrt{5}\\$

3 0

3 years ago