Question

Task 1 (7 points). The probability of successful solving a Math test by the first student is 0.9, by the second student is 0.6, by the third student is 0.8. What is the probability of solving this test by: a) one student only; b) only the third student; c) all of the students; d) at least one of students? Task 2 (7 points). The pizza delivery department receives 75% brand pizza orders. Find the probability that among 100 received orders there will be (a) 72 brand pizza orders; (b) from 70 to 78 brand pizza orders. (c) Find the most probable number of brand pizza orders. Task 3 (8 points). The integral function of X is given: o, X2 F(x)= 2 - 4x +4) 2<x56. Calculate: a) the density function f(x); b) the 16 1, x>6 mathematical expectation M(X) and the variance; c) the probability P(4< X <7). Task 4 (8 points). The continuous statistical series is given in the table: (x,x) 13 - 15 15-17 17-19 19-21 21 - 23 8 23 6 3 a) Find the mean (xs), the variance (S) and the root-mean-square deviation (S) for this sample. b) Plot the histogram and make the assumption about the distribution law. c) Find the confidence interval for the population mean with the probability P=0,95 and P=0,99. d) Make an analysis of the obtained values. Task 5 (10 points). Data: 2x=1432, Ły=1714, Ey? = 29553, n=1 n=100. E xy = 24816, 2x² = 21756, a) Construct a pair linear equation of a regression: İx = bo +bıx and Make an analysis of coefficients. b) Calculate a correlation coefficient r, a determination coefficient R2 and explain obtained results. c) Verify a hypothesis about a statistical significance of a linear correlation coefficient at the significance level a=0,01. 10 It was approved at the meeting of the department of higher mathematics and economic mathematical methods Protocol No 10 from May 15, 2019 The head of the department prof. L. Malyarets The lecturer doc. le. Misiura

Answer 1

Please give the questions separately.
0.9 X 0.4 X 0.2 t Olx 0.6 X 0.2 t 0.! XO 4X03 Tak A: P(A) = 0.9 P(c) = 0.8 A, B and Care indpht P(B) = 0.6, P(A): L (*): -1, (c): 2. a) Plane student only solves the problem) PLAB CC) + PCA*BCC) + PCA"BⓇC) P(ABC) : PIA )&(B) ECG 0.072t 0.012 + 0.032 0.11 6 by Plonly the third slüdent selves)= P(AⓇB°c) 0.18 0.48 0.8 0.032

plall of the studente solve) = P(ABC) 0.9% 0.6 408 - 0.432 (1) Plat least one of the students solve) : 1- Plenone solve) 1-P(ABC) . 1-60.1 X 0.44 X 0:2) 0-008 0-992.