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3 years ago

3. The sum of three consecutive numbers is 42. What are the numbers?

Mathematics

1 answer:

Zanzabum3 years ago

3 0

Answer:

13 + 14 + 15

Step-by-step explanation:

n + (n + 1) + (n +2) =42

n + n + n + 1 + 2 = 42

3n + 3 = 42

(subtract 3 from both sides)

3n = 39

(divide both sides by 3)

n = 13

(solve)

n + (n + 1) + (n +2) =42

13 + (13 + 1) + (13 + 2) = 42

13 + (14) + (15) = 42

13, 14, 15

(Hope this helps, have a nice day!)

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Answer:

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Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

$\mu = \frac{3X_{1} + 4X_{2} }{8}$

Now

Bias for the estimator = E(μ bar) - μ

= $E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5$

= $\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5$

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= $\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136$

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