Answer: 45b^4/32
Step-by-step explanation: First multiply the two fractions
15b^3y(3b)/8y x 4
Multiply 3 by 15
45b^3yb/8y x 4
Raise b to power of 1
45(b^1b^3)y/8y x 4
Use power rule to combine exponents
45b^1+3 y/8y x 4
Simplify
45b^4y/32y
Cancel common factor of y
45b^4/32
Answer:

Step-by-step explanation:
![\sqrt[3]{-\frac{1}{512}}=\frac{\sqrt[3]{-1}}{\sqrt[3]{512}}=\frac{-1}{8}=-\frac{1}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%5Cfrac%7B1%7D%7B512%7D%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B-1%7D%7D%7B%5Csqrt%5B3%5D%7B512%7D%7D%3D%5Cfrac%7B-1%7D%7B8%7D%3D-%5Cfrac%7B1%7D%7B8%7D)
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
= 
= 
= ![\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)
= 
= 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311