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love history [14]
3 years ago
9

Suppose you have an experiment where you flip a coin three times. You then count the number of heads. a.) State the random varia

ble. b.) Write the probability distribution for the number of heads. c.) Draw a histogram for the number of heads. d.) Find the mean number of heads. e.) Find the variance for the number of heads. f.) Find the standard deviation for the number of heads. g.) Find the probability of having two or more number of heads. h.) Is it unusual to flip two heads

Mathematics
1 answer:
coldgirl [10]3 years ago
6 0

Answer:

The answer to each point is below

Step-by-step explanation:

We will solve point by point:

a)  We have to:

Random variable X = number of heads

Let, H => heads, T => tails

b) We have that the combinations are

TTT, TTH, THT, THH, HTT, HTH, HHT, HHH

Number of Heads (X)  0     1      2     3

Probability (P)             1/8   3/8  3/8   1/8

c) attached the histogram.

d)  We have the following:

Mean = E (X) = 0 * 1/8 + 1 * 3/8 + 2 * 3/8 + 3 * 1/8

m = 1.5

The mean is 1.5

e) E (X ^ 2) = 0 * 1/8 + 12 * 3/8 + 22 * 3/8 + 32 * 1/8 = 3

Variance = E (X ^ 2) - (E (X)) ^ 2

Var = 3 - (1.5) ^ 2

Var = 0.75

The variance is 0.75

f) standard deviation = (Var) ^ (1/2) = (0.75) ^ (1/2) = 0.866

sd = 0.866

the standard deviation is 0.866

g) P (2 or more heads) = 3/8 + 1/8 = 0.5

The probability is 50%

h)  P (two heads) = 3/8 = 0.375

It is likely that out of 8 times of 3 flips, 3 times we can observe two heads out of 3, therefore it is not unusual.

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Andreas93 [3]

Answer:

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Step-by-step explanation:

You can use the center of a circle to write an equation in vertex form. Vertex form is (x-h)^2+(y-k)^2 = r^2 and the vertex is (h,k). Notice (h,k) are the opposite sign in the equation then as the point.

Here h = -4 and k = 3. Substitute these values and the value r = 5.

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2 years ago
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lara [203]

<u>Complete Question with table is attached</u>

<u>Answer:</u>

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<u>Step-by-step explanation:</u>

The figure attached clearly shows the ratio of his earnings and savings. We have to find what would be the savings amount if he earn $120.00. So, first we have to calculate the percentage of ratio of his earnings and savings. As per the data given in the figure,

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3 years ago
When is sin(np) even or odd.
forsale [732]

Answer:

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Step-by-step explanation:

The concepts of odd and even apply only to integers .y = cos x is always going to be even, because sin(np) is an even function.

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2 years ago
How do I do this I don't understand
oksian1 [2.3K]
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