Answer:
-12x^2 + 11xy - 2y^2
Step-by-step explanation:
 
        
                    
             
        
        
        
300 dollars, 15x20 because they count any fraction as a foot, so is like you are going to buy 20 foot of carpet.
        
             
        
        
        
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
 
        
             
        
        
        
Answer:  The probability of rejecting the null hypothesis, when it is true, is 5%.
Step-by-step explanation:
We know that the level of significance ( denoted as  ) is generally the probability of rejecting the null hypothesis when it is true.
 ) is generally the probability of rejecting the null hypothesis when it is true.
Therefore , If the level of significance (\alpha[/tex] ) 0.05, then it means that it is the probability of rejecting the null hypothesis when it is true.
i.e. The probability of rejecting the null hypothesis when it is true= 0.05
In percent : 
Hence, the correct option is : The probability of rejecting the null hypothesis when it is true is 5%.
 
        
             
        
        
        
Answer:
Step-by-step explanation:
f(0) = 3
of(5) = -1
f(3) = 2
5
-3 -2 -14
1
2
3
4
5
f(2)= -2