Question
Download Solution PDFLet X be the discrete random variable with PMF (x) = \(\dfrac{1}{2^x}\); x = 1,2,3,.... The value of P(X > 4) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
PMF(x) = 1/2x, x = 1, 2, 3 -----
Formula
P(X > 4) = 1 – P(X ≤ 4)
Calculation
P(X > 4) = 1 – P(X ≤ 4)
⇒ 1 – [P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)]
⇒ 1 – [1/21 + ½2 + ½3 + ½4]
⇒ 1 – [1/2 + ¼ + 1/8 + 1/16]
⇒ 1 – [(8 + 4 + 2 + 1)/16]
⇒ 1 – [15/16]
⇒ (16 – 15)/16
∴ The value of P(X > 4) is 1/16
Probability mass function or PMF is defined as the set of ordered pair [x, f(x)] if for each possible outcome x, f(x) satisfies the following condition
F(x) ≥ 0
∑ f(x) = 1
Last updated on Jul 9, 2025
-> The SSC CGL Notification 2025 for the Combined Graduate Level Examination has been officially released on the SSC's new portal – www.ssc.gov.in.
-> Bihar Police Admit Card 2025 Out at csbc.bihar.gov.in
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> The AP DSC Answer Key 2025 has been released on its official website.
-> The UP ECCE Educator 2025 Notification has been released for 8800 Posts.