Probability

July 13, 2015 by Arjun Suresh 7 Comments

Syllabus

Random variables.
Uniform, normal, exponential, poisson and binomial distributions.
Mean, median, mode and standard deviation.
Conditional probability and Bayes theorem.

“No changes since 2016”

Book

Sheldon Ross

Video

Web Links

Previous Year Questions

http://gateoverflow.in/questions/mathematics/probability

Important Questions

http://gateoverflow.in/blog/18/important-questions-in-probability

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Answered: UGCNET-Oct2020-II: 72

Serial Line IP (SLIP)--->Data Link layer ( Serial Line Internet Protocol (SLIP) , Compressed SLIP (CSLIP) , High-level Data Link Control (HDLC) , Point‑to-Point Protocol (PPP) , Frame Relay, and Ethernet. Border Gateway Protocol (BGP)-->Network layer (Routing protocol) User Data Protocol (UDP)---->Transport Layer Simple Network Management Protocol--→Application layer Hence correct ans is option B [...]

Answered: UGCNET-Oct2020-II: 69

The Means-end-analysis technique is a strategy to control search in problem-solving. Given a current state and a goal state, an action is chosen which will reduce the difference between the two. The action is performed on the current state to produce a new state, and the process is recursively applied to this new state and the goal state. Constraint satisfaction problems are mathematical questions defined as a set of objects whose state must satisfy a number of constraints. The general idea of Branch and bound algorithm is a BFS-like search for the optimal solution, but not all nodes get expanded . Rather, a carefully selected criterion… [...]

Answered: Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 29 (Page No. 468)

Answered: Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 29 (Page No. 468)

Yes, in this case deadlock is possible. Take a simple resource deadlock graph. Just reinterpret the resources as messages. Like P1 is wating for message M2 from P2. P2 is waiting for message M1 from P1. Since both the waits are blocking, there is a deadlock. [...]

Answered: GATE2006-72

If you generalise this question, I have devised a formula For intersection to be exactly k elements k [...]

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Answer is – 54 let’s fix the W2(A) now to preserve the read write conflict R4,R2,R3(A) should come before it does not matter in which order so total total number of combination will be 3! but we have also W1(B) here which can come before or after W2(A) it does not matter. so number of cases W1(B) can be put before W2(A) is 4! = 24 along with R4,R2,R3(A) and W2(A) ,R3(B),W2(B) can be placed after them is 2 keeping dependency of R3(B)--->W2(B) AND W2(A)--->W2(B) HENCE number of schedule possible till now is 24 x 2 = 48 number of cases W1(B) can be put after W2(A) is 1 keeping dependency of W1(B)----->R3(B)---->W2(B) AND W2(A)--->W2(B) W2(A)--->W2(B) and R4,R2,R3(A) can be arrange in 3! = 6 ways so total possible schedule =… [...]

Answered: GATE2004-79

Answered: GATE2004-79

This is the best explanation I can provide to you [...]

Answered: NIELIT 2019 Feb Scientist D - Section D: 30

$\textrm{Given that:}$ $log_{10}(2^x+x-41)=x(1-log_{10}5)$ $\because log_aa=1$ $\textrm{We can use this property here, $log_{10}10=1$}$ $\implies$ $log_{10}(2^x+x-41)=x(log_{10}10-log_{10}5)$ $\implies$ $log_{10}(2^x+x-41)=x(log_{10}(\frac{10}{5}))$ $(\because log_ax-log_ay=log_a(\frac{x}{y}))$ $\implies$ $log_{10}(2^x+x-41)=x(log_{10}2)$ $\implies$ $log_{10}(2^x+x-41)=log_{10}2^x$ $(\because log_ax^n=n*log_ax)$ $\textrm{compair both side we get:}$ $\implies$ $2^x+x-41=2^x$ $\implies$ $x=41$ $\textrm{Option b is correct.}$ [...]

Answered: NIELIT 2019 Feb Scientist C - Section D: 19

$\textrm{Given that:}$ $x=\frac{\sqrt10+\sqrt2}{2},y=\frac{\sqrt10-\sqrt2}{2}$ $\textrm{first find $x^2+xy+y^2$}$ $\implies$ $x^2+xy+y^2+xy-xy$ $\implies$ $x^2+2xy+y^2-xy$ $\implies$ $(x+y)^2-xy….(1)$ $\textrm{Let find x+y first:}$ $\implies$ $\frac{\sqrt10+\sqrt2}{2}+\frac{\sqrt10-\sqrt2}{2}$ $\implies$ $\frac{2*\sqrt10}{2}$ $\implies$ $x+y=$ $\sqrt10...(2)$ $\textrm{Let find x*y:}$ $\implies$ $\frac{\sqrt10+\sqrt2}{2}*\frac{\sqrt10-\sqrt2}{2}$ $\implies$ $\frac{(10-2)}{4}$ $\implies$ $x*y=$$2...(3)$ $\textrm{Substitute eq (2) &(3) into (1), we get:}$ $\implies$ $(\sqrt{10})^2-2$ $\implies$ $8$ $\textrm{Now find l$og_2(8)$,which is equal to 3}$ $\textrm{Option D is correct.}$ [...]

Answered: NIELIT 2019 Feb Scientist C - Section C: 19

$\textrm{Given that: }$ $a^x=b ….(1)$ $b^y=c ….(2)$ $c^z=a….(3)$ $\textrm{taking log in above equations we get:}$ $\implies$ $xlog_2a=log_2b$ $\implies$ $x=\frac{log_2b}{log_2a}….(4)$ $\textrm{in the same way}$ $y=\frac{log_2c}{log_2b}….(5)$ $z=\frac{log_2a}{log_2c}…..(6)$ $\textrm{multiply equations (4),(5),(6).}$ $\implies$ $x*y*z=\frac{log_2b}{log_2a}*\frac{log_2c}{log_2b}*\frac{log_2a}{log_2c}$ $\implies$ $x*y*z=1$ $\textrm{Option C is correct.}$ [...]

Logical reasoning

Each question below contains six statements followed by four sets of combinations of three; Choose the set in which the statement are logically related. A. Final year students would like a good career. B. All final year students are eligible as candidates for MBA entrance examination. C.Final year students are eligible for a good career. D. Some of those who are candidates for an MBA entrance examination are final year students. E. All those eligible as candidates for an MBA entrance examination are eligible for a good career. F. All those who would like a good career are entitled to… [...]

Answered: NIELIT 2019 Feb Scientist D - Section C: 21

Answered: NIELIT 2019 Feb Scientist D - Section C: 21

Now, if 6th reading is x, the x+x+3+x+8= 93.8 after solving, x=27.6 [...]

Answered: NIELIT 2019 Feb Scientist C - Section C: 15

Difference = 500 5% = 500. 100% = (500 *100)/5 = 10000. 100% is the labeled price. So, TV price = 10000 - 20% of 10000 = 80% of 10000 = 8000. [...]

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