I need help with this question.

Let X equal the number of flips of a fair coin that are required to observe

Nataliya [291]

Answer:

(a) I attached a photo with the diagram.

(b) $f(x) = \big( \frac{1}{2} \big)^{x-1}$

(c) 1/4

(d) 4

(e) $k^2/2$

Step-by-step explanation:

(a) I attached a photo with the diagram.

(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.

To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.

1 - Your first outcome is HEADS and all the others are different except the last one.

2 - Your first outcome is TAILS and all the others are different except the last one.

Therefore the probability of the event is

$f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}$

(c)

P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.

$E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}$

(d)

Remember that this is a geometric distribution therefore

$E[X] = p/(1-p)$ , in this case $p = 1/2$ so $E[X] = 1$ and

$E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4$

Also

(e)

This is a geometric distribution so its variance is

$Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2$

And using properties of variance

$Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2$

3 0

4 years ago

Anna walked 8 miles in 3 hours. Juan walked 14 miles in 5 hours. Are these rates in proportion?

Veronika [31]

These rates are not in proportion. Juan walked faster.

Explanation:

First, we want to make these ratios to have the same denominator so we can compare the numerators. To do this, do 3x5 and 8x5 to get 40:15. Then, we do 5x3 and 14x3 to get 42:15. Now we can just compare the numbers 40 and 42, and since 42 < 40, we know Juan walked faster.

5 0

3 years ago

Julianna has 32 pieces of candy in a jar. Julianna only has 2 kinds of candy, jolly ranchers and Twix. For every 4 Twix bars, sh

nexus9112 [7]

Answer:

the data set seems wrong, since for every 4twix bars, she had 2 pieces of jolly ranchers; so ratio 4 twix bars : 2 ranchers is to be use but it wouldn't work, it can only work for the first 30 candies ( 20twix bars and 10 ranchers) so the last 2 candies( if following the ratio will be 4/3 for the twix bars and 2/3 for the ranchers)

6 0

3 years ago

Which simplified ratio correctly compares 30 inches to 2 feet?

olchik [2.2K]

Answer:

15:1

Step-by-step explanation:

30/2=15

2/2 = 1

15:1

4 0

3 years ago

In the supermarket, there is a scale that measures the weight of fruit and vegetables. The needle is 24 cm long and it rotated 9

Mumz [18]

We find the length of the arc followed by the needle. For this, we first need to convert the subtended angle to radians:
96/∅ = 180/π
∅ = 1.68 rad
S = r∅
S = 24 x 1.68
Distance covered by needle = 40.32 cm

4 0

4 years ago

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