here are some numbers 8 11 13 18 25 37 , 8 13 18 is an arithmetic progression and the rule is to add 5 use 3 of the numbers to m
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The y-intercept of linear function (f- g)(x) is (0,9)
<h3>How to determine the y-intercept?</h3>The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
So, we have:
Evaluate
f(x) = -2x + 3
Also, we have:
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
Read more about linear functions at:
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Answer:
Bias for the estimator = -0.56
Mean Square Error for the estimator = 6.6311
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
Now
Bias for the estimator = E(μ bar) - μ
=
=
=
=
=
= 3.9375 - 4.5
= - 0.5625 ≈ -0.56
∴ we get
Bias for the estimator = -0.56
Now,
Mean Square Error for the estimator = E[(μ bar - μ)²]
= Var(μ bar) + [Bias(μ bar, μ)]²
=
=
=
=
=
=
=
= 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311
Answer:
Step-by-step explanation:
Given that there is a t distribution with 7 degrees of freedom.
P(-1.29 < t < 1.29)=1-0.2380
=0.7620
b) Now there is a different t distribution with 18 df.
When
c=-1.733