Fr j K rubbghhhghbvvv it’s is B
Area formula for a triangle is 1/2BxH
B=15
H=10
1/2(15)= 7.5
7.5 x 10= 75
So the area is 75 square cm :)
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
![\mu = \frac{3X_{1} + 4X_{2} }{8}](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%5Cfrac%7B3X_%7B1%7D%20%2B%204X_%7B2%7D%20%20%7D%7B8%7D)
Now
Bias for the estimator = E(μ bar) - μ
= ![E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5](https://tex.z-dn.net/?f=E%28%20%5Cfrac%7B3X_%7B1%7D%20%2B%204X_%7B2%7D%20%20%7D%7B8%7D%29%20-%204.5)
= ![\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5](https://tex.z-dn.net/?f=%5Cfrac%7B3E%28X_%7B1%7D%29%20%2B%204E%28X_%7B2%7D%29%7D%7B8%7D%20-%204.5)
= ![\frac{3(4.5) + 4(4.5)}{8} - 4.5](https://tex.z-dn.net/?f=%5Cfrac%7B3%284.5%29%20%2B%204%284.5%29%7D%7B8%7D%20-%204.5)
= ![\frac{13.5 + 18}{8} - 4.5](https://tex.z-dn.net/?f=%5Cfrac%7B13.5%20%2B%2018%7D%7B8%7D%20-%204.5)
= ![\frac{31.5}{8} - 4.5](https://tex.z-dn.net/?f=%5Cfrac%7B31.5%7D%7B8%7D%20-%204.5)
= 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
= ![Var( \frac{3X_{1} + 4X_{2} }{8}) + 0.3136](https://tex.z-dn.net/?f=Var%28%20%5Cfrac%7B3X_%7B1%7D%20%2B%204X_%7B2%7D%20%20%7D%7B8%7D%29%20%2B%200.3136)
= ![\frac{1}{64} Var( {3X_{1} + 4X_{2} }) + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20Var%28%20%7B3X_%7B1%7D%20%2B%204X_%7B2%7D%20%20%7D%29%20%2B%200.3136)
= ![\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%28%20%5B%7B3Var%28X_%7B1%7D%29%20%2B%204Var%28X_%7B2%7D%29%5D%20%20%7D%29%20%2B%200.3136)
= ![\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B%7B3%2857.76%29%20%2B%204%2857.76%29%7D%5D%20%20%7D%20%2B%200.3136)
= ![\frac{1}{64} [7(57.76)}] } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B7%2857.76%29%7D%5D%20%20%7D%20%2B%200.3136)
= ![\frac{1}{64} [404.32] } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B404.32%5D%20%20%7D%20%2B%200.3136)
= ![6.3175 + 0.3136](https://tex.z-dn.net/?f=6.3175%20%2B%200.3136)
= 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311
Answer:
Step-by-step explanation:
B.(10,1)
first you turn the fractions into inproper fractions by multiplying the whole number by the denomonator and adding the numerator
4×4=16
16+3=19
19/4
4×7=28
28+1=29
29/7
keep the denomonators the same. now that you've converted them into inproper fractions you can multiply them
19/4 × 29/7=551/28
there is no way to simplify this answer so this is the final answer