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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forwardSuppose X = number of direct injuries occurring in a fire incident. Its PMF is given by x 0 1 2 3 4 5 6 7 f(x) 0.08 0.08 0.09 0.14 0.18 0.18 0.16 0.09 0.06 Determine the mean and variance of the number of direct injuries occurring in a fire incident. 8 0.06arrow_forwardThe sample correlation coefficient is equal to the covariance of x and ydivided by the square root of the product of sx2 times sy2. True Falsearrow_forward
- Given f(x) = { (x2+1)/30; x = -2,-1,0,1,2 0; elsewhere ] Find the mean and variance of X.arrow_forwardThe mean is equal to of cellular phones of sold per day is therefore, it means that the average number To find the variance complete the table below: P(x) x2 - P(x) .2 X•P(x) 15 0.30 4.5 18 0.20 3.6 19 0.20 3.8 20 0.15 22 0.15 3.3 ix2 . P(x) = g? = ) [x² · P(x)] - u² = %3D %3D %3D while herefore, the variance of a probability distribution is equal to ne standard deviation is equal to such a igher ngarrow_forwardQ1. Let X; and S be the mean and variance of independent random samples of size ni from populations with mean H; and variance of (i = 1,2), respectively where u, = 20. of = 9, n1 = 36 and u2 = 18, ož = 16, n2 = 49. Find (- a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S} > s3) = 0.80 e) P(X1 – X2 > 0.2336) n P(SE/S글 > 0.8368) %3Darrow_forward
- The pdf of random variable X is given as ƒx(x) = Find the i) Mean ii) Mean of the square [0.3507√x 0arrow_forward(a):The no. of industrial injuries per working week in a particular factory is known to follow a distribution with p(x;3). In a particular week there will be: Less than two incidents More than four incidents Find mean and variance of the distribution. P(x>1/2)arrow_forwardCustomers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with P(A) = 0.3, P(B) = 0.3, and P(C) = 0.4. (a) Among the next 210 customers, what are the mean and variance of the number who pay with a debit card? E(X) = V(X) = Explain your reasoning. This answer has not been graded yet. (b) Answer part (a) for the number among the 210 who don't pay with cash. E(X) = V(X) =arrow_forwardThe correlation between X and Y Select one or more: a. is the covariance squared b. cannot be negative since variances are always positive. c. is given by corr(X, Y) = cov(X,Y)/var(X)var(Y)cov(X,Y)/var(X)var(Y) d. can be calculated by dividing the covariance between X and Y by the product of the two standard deviationsarrow_forwardSuppose that y, is an independent response variable (i = 1.....n) with mean, such that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3 is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pi) (Yi - Pi) + Ni w₁ = [V (pi) (g'(pi))²]-¹ 8 where g'(μ) = 9(μ) (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?arrow_forward(x₁,...,xn) be a data set, and denote its sample standard deviation with s. Let yį = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., Yn). (b) Show that Median(y) = a. Median(x) + b. Let x = (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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