Questions in Grade High-school

Questions in Grade High-school

[Done] b) [tex]4^{-x} = \frac{1}{16}[/tex] c) [tex]\frac{1}{5^n} = 125[/tex]

[Done] A thermometer measures in centigrade scale. It is of which type of the following? a. Interval Scale b. Ordinal Scale c. Ratio Scale d. Nominal Scale

[Done] cos 15° = (√6 + √2) / 4

[Done] For all problems on this page, suppose you have data X_1, ..., X_n ~ N(0, 1) that is a random sample of identically and independently distributed standard normal random variables. Useful facts: For a standard normal random variable X_1, we have: E[X] = 0, E[X^2] = 1, E[|X|] = sqrt(2/pi) approx 0.8 The i.i.d. assumption Suppose X_1 is an observation for Bob, X_5 is an observation for Alice, X_7 is an observation for Charlie. Using the following facts about Bob: P(-2 < X_1 < 2) approx 0.95 and P(-sqrt(2) <= X_1 <= sqrt(2)) approx 0.75, compute the probability P(-2 < X_5 < 2, -2 < (X_7)^5 < 2) (Enter the probability P(-2 < X_5 < 2, -2 < (X_7)^5 < 2) or if the probability is not determined uniquely, then enter -1.) P(-2 < X_5 < 2, -2 < (X_7)^5 < 2) = ________ Sample mean Consider the sample mean: bar{X_n} = (1/n)(X_1 + X_2 + ... + X_n). What are the mean E[bar{X_n}] and variance Var[bar{X_n}] of bar{X_n}? E[bar{X_n}] = ________ Var[bar{X_n}] = ________ What kind of distribution does bar{X_n} follow? - Gaussian - Student t - Chi square - Gamma - nonparametric Quantiles Consider the quantile Q_{n, alpha} of order 1 - alpha for the random variable bar{X_n}, that is, the number Q_{n, alpha} such that P(bar{X_n} <= Q_{n, alpha}) = 1 - alpha, 0 < alpha < 1. For alpha < 0.5, as the sample size n increases, does the quantile Q_{n, alpha}: - Increase - Decrease - Stay the same - Oscillate

[Done] Select the correct answer. Which of the following represents a constant from the expression given? [tex]$15 x^2+2 x+9$ A. 2 B. 9 C. 15 D. 24

[Done] What is the slope of the line whose equation is $y-4=\frac{5}{2}(x-2)$?

[Done] Which of the following is the solution of [tex]$5 e^{2 x}-4=11 ?$[/tex] A. [tex]$x=\ln 3$[/tex] B. [tex]$x=\ln 27$[/tex] C. [tex]$x=\frac{\ln 3}{2}$[/tex] D. [tex]$x=\frac{3}{\ln 3}$[/tex]

[Done] Which term describes a pure substance that is made up of only one type of atom? A. matter B. rock C. compound D. element

[Done] Within a major, students can choose to study a specific area. This is called a(n): A. general study. B. elective. C. minor. D. specialization.

[Done] The Battle of Saratoga was particularly significant because A. this quick victory showed American superiority. B. it resulted in an alliance between the Americans and the French. C. it demonstrated General Burgoyne's incompetence. D. the British routed the Americans.