Question

- Question 1 1 point The following function is a pdf: 2 - x) 0 <3 < 2 f (x) = { 10" 1 0 otherwise True False - Question 2 1 point Number Help A card is drawn from a standard deck of 52 cards. What is the probability that the card belongs to the set {4,5..., 8}? decimal accuracy please.) -ZC Number

Answer 1

Note: as per rules first question of multiple questions is also allowed to solve.So i have solved for first question. Formulas: 1) The function f(x) is said to be PDF if f(x) > 0 and f(x) dx = 1 Given that the PDF f (x) = s * * (2 — «) 0<x<2 1 0 otherwise

Q1) Now we have to check that f(x) is a density function or not. 3x > 0 for 0 < x < 2 and (2 - x) 2 0 for 0 sxs2 = x(2 - x) > 0 for 0 sxs2 =f(x) > 0

10 f(x) dx = x(2 – x) dx (:: 0 sxs2) - # (S«(2 – x) dx) 6). = + (1©(2x – x2) dx) = (2x dx – Lịx? dx) -(20.- 0) (264-99)-6-)) 1(2(2) – () = t: (4-9) = io (4-) = o C

=ff(x) dx #1 =f(x) is not a PDF. .: False is the answer.