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Tpy6a [65]
3 years ago
6

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

0 bit and a 1 bit are equally likelyb) the probability that a bit is a 1 is 0.6c) the probability that the i-th bit is a 1 is 1/(2^i) for i=1,2,3,...,10
Mathematics
1 answer:
lara31 [8.8K]3 years ago
3 0

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

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The y -intercept of 5x - 3y = 15 is (0, -5)

<h3><u>Solution:</u></h3>

Given equation is 5x - 3y = 15

<em><u>To find: x - intercept and y -intercept</u></em>

The x intercept is the point where the line crosses the x axis. At this point y = 0

The y intercept is the point where the line crosses the y axis. At this point x = 0.

<em><u>Finding x - intercept:</u></em>

To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x

So put y = 0 in given equation

5x - 3(0) = 15

5x = 15

x = 3

So the x - intercept is (3, 0)

<em><u>Finding y - intercept:</u></em>

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y

So put x = 0 in given equation

5(0) - 3y = 15

-3y = 15

y = -5

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Step-by-step explanation:

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We have to trade 5 bunnies for a donkey.

Solution:

To calculate how many bunnies could be exchanged for a donkey, we have to multiply the exchange rates of each animal/bird.

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One pig = 2/3 donkeys (0.67 donkeys).

On multiplying all of the above rates we get,

0.75*0.4*0.67=0.2

Since we now know a bunnies worth is 0.2 donkey

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Which statements are true about the interquartile range? Select all that apply.
PilotLPTM [1.2K]

Answer:

The true statements are:

B. Interquartile ranges are not significantly impacted by outliers

C. Lower and upper quartiles are needed to find the interquartile range

E. The data values should be listed in order before trying to find the interquartile range

Step-by-step explanation:

The interquartile range is the difference between the first and third quartiles

Steps to find the interquartile range:

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B. Interquartile ranges are not significantly impacted by outliers ⇒ True <em>(because it does not depends on the smallest and largest data)</em>

<em />

C. Lower and upper quartiles are needed to find the interquartile range ⇒ True <em>(because IQR = Q3 - Q2)</em>

<em />

D. A small interquartile range means the data is spread far away from the median ⇒ NOT true (<em>because a small interquartile means data is not spread far away from the median</em>)

E. The data values should be listed in order before trying to find the interquartile range  ⇒ True <em>(because we can find the interquartial range by finding the values of the upper and lower quartiles)</em>

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