Question

QUESTION 4 4.1. Name and discuss four probability distributions, highlight their characteristics, how they are similar to me another, and how they differ from one another 4.2. According to StatsSA, the unemployment rate in South Africa as of 2018 has risen to 28%. For a randomly selected group consisting of eight South Africans, what is the probability that at least two are unemployed 4.3. According to the latest statistics, the average take-home pay in South Africa increased in real terms by 44% year-on-year to reach R14,500, with a standard deviation of R4000. You have been offered a job, and wish to considering that you are adequately experienced and qualified) suggest a salary of R15 500. What is the probability that they will offer you a salary of more than R15 500? QUESTION 5 (20) 5.1. You are wanting to invest. The following table represents the portfolio for shares. Use the Laspeyres and Paasche's price indices to determine how the shares fared. Conclude your calculations with a summary of how the shares faired, and whether or not you would consider investing in any of the company's 52 Share Base Year Po 90 120 210 150 220 180 250 2018 P1 180 175 205 91 125 212 220 B 5.2. You are conducting an analysis of the inflation rate over the past couple of months in effort to identify whether or not South Africa is improving economically, or not. You collect data over the past ten months, it looks as follows: Year Inflation (in %) ul. 18 Aug-182 Sep-18 3 Oct-184 Nov-185 Dec-18 L Jan-19 Feb-195 Mar-19 2.95% 2.70% 2.28% 2.52% 2.18% 1.91% 1.55% 1.529 1 B6X Smook 2.00% 2.95% Apr-19 10 May-19 5.2.1 5.2.2 5.23 5.24 Draw a scatter diagram of the data above. Calculate the correlation coefficient Interpret the results of the correlation with reference to the inflation rates between July 18-May Calculate the regression equation LANDBOOK: JULY 2013 TE HANDBOOK: JULY 2019 INTAKE

Answer 1

Uniform distribution, exponential distribution, Gamma dishibution, normal distribution beto distribution are diferent probability distributions. 1 Uniform Distribution let x urab) lp.d.z is fixes = 10 (x) bra ft. 6) - where I canx) = f ; ;} acach ; otherwise 6-a .a<3<b ; C. D. F is flu) = (x-a b-a acueb usa uzb nential Distribution - Exp (2) p.d. is f(x) = xe xx I xxo x30 otherwise I a.D.F is F (x) = { i-e od 10 otherwise 3) Gamma distribution X Gamma (@= scale, ß- shape) fon) of dB pred zB & B70x70 otherwise

Grammatt, IR x 9 Grammala, ß) then for c>o ex then cx Gammafa, & 23 x, X... xo are iid exp(a) then şi Gammale) 28 x - x² then x Garman (%, 2%) 4) normal distribution - X Nill, 2. pdf is l location : 0 =scale fin) = - exp21 (x-1 27. 127 82 expl-1 (x-ag 20? Her MEIR - Normal is symmetric unimodal distribution. X, N1, 2) X2 Nrel, ²) are inde then x + x₂ + Nieliteli 0, 22 +298,022 Y coir(x,x) M.G-F.04 x Not is then Mxt) for eap elt +2rty o c=constant el ex x+c Nice, c22) Ncute, s2)