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11111nata11111 [884]
3 years ago
15

If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H) and tails (T). Supposethe random variable X repre

sents the number of heads in a sequence. Construct the probabilitydistribution for X.
Mathematics
1 answer:
postnew [5]3 years ago
8 0

Answer:

The probability distribution of X is:

P(x=0)=0.0625\\\\P(x=1)=0.25\\\\P(x=2)=0.375\\\\P(x=3)=0.25\\\\P(x=4)=0.0625\\\\

Step-by-step explanation:

"Tossing a coin and getting H" can be modelled as a Bernoulli random variable. The variable X is a sum of 4 of this Bernoulli variables, we can model X as a binomial random variable, with p=0.5 and n=4.

The values X can take are: 0, 1, 2, 3 and 4.

The values of this probability are calculated as:

P(x=0) = \binom{4}{0} p^{0}q^{4}=1*1*0.0625=0.0625\\\\P(x=1) = \binom{4}{1} p^{1}q^{3}=4*0.5*0.125=0.25\\\\P(x=2) = \binom{4}{2} p^{2}q^{2}=6*0.25*0.25=0.375\\\\P(x=3) = \binom{4}{3} p^{3}q^{1}=4*0.125*0.5=0.25\\\\P(x=4) = \binom{4}{4} p^{4}q^{0}=1*0.0625*1=0.0625\\\\

Where

p: is the probability of tossing a coin and getting a Heads

q: is the probability of tossing a coin and not getting a Heads.

The binomial number is a way to calculate the possible combinations of getting a certain amount of heads.

For example, in 4 tosses, there are 6 ways or combinations of getting 2 heads and 2 tails:

\binom{4}{2}=\frac{4!}{2!(4-2)!}=\frac{24}{2*2}=6

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2 years ago
To factor the quadratic expression x^2−8x−10 by completing the square, what value would be added? A. 64 B. 8 C. 16 D.-16
Elan Coil [88]

Answer:

C

Step-by-step explanation:

When completing the square, we essentially want to create a perfect square trinomial by adding a constant.

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The value we would add would be 16.

The answer is C.

Further notes:

To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:

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The expression inside the parentheses is now a perfect square trinomial. Factor it:

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Use a calculator or a square root table to approximate to the nearest thousandth
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Answer:

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Here we have to calculate the square root of a certain number using the help of the calculator or a square root table.

The given expression is - \sqrt{ 171 }.

Now, using calculator \sqrt{ 171 } = 13.076696

Now,  - \sqrt{ 171 } = - 13.076696

So, approximate value to the nearest thousandth is - 13.077 ( Answer )

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2 years ago
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