Probability and Statistics Quiz

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Questions and Answers

What can be inferred about the relationship between properties A and B if Q = (0.5)?

  • A and B are not independent. (correct)
  • A and B are independent.
  • A and B are partly positive.
  • A and B are partly negative.

What does the notation lim x → 1 signify?

  • X must be less than 1.
  • X approaches 1 from any direction. (correct)
  • X is equal to 1.
  • X must be greater than 1.

Which of the following best represents a random variable?

  • Number of heads obtained when a coin is tossed five times. (correct)
  • Height and weight of individuals.
  • The time of sunrise in a specific city.
  • Daily stock market closing prices.

Given E(x) = 7.5 and E(y) = 7.5, what value would E(x + y) yield?

<p>15 (A)</p> Signup and view all the answers

What is the expected value of a random variable X if P(X = 1) = 0.3 and P(X = 2) = 0.7?

<p>1.7 (B)</p> Signup and view all the answers

હું શું કહી શકું છું જો ગુણાત્મક સિલસિલા Q = (0.5) છે?

<p>A અને B સ્વતંત્ર નથી. (B)</p> Signup and view all the answers

Lim x → 1 નું મહત્વ શું છે?

<p>X = 1 (C)</p> Signup and view all the answers

નીચેના પૈકી કયો રેંડમ ચકરોનું ઉદાહરણ છે?

<p>ત્રણ વખત સેકડા પડતા પાંગળાના સંખ્યા (C)</p> Signup and view all the answers

જો બે રેંડમ ચકરો x અને y માટે E(x) = 7.5 અને E(y) = 7.5 છે, તો E(x + y) શું હશે?

<p>15 (D)</p> Signup and view all the answers

જો રેંડમ ચકરો X માટે X = 1 ની સંભવના 0.3 છે અને X = 2 ની સંભવના 0.7 છે, તો તેનો અપેક્ષિત મૂલ્ય શું બને છે?

<p>1.7 (C)</p> Signup and view all the answers

Flashcards

lim x → 1

Means the value of x approaches 1, but is not necessarily 1.

Q = 0.5 qualitative relationship

Indicates properties A and B are not independent.

Expected value of X (P(X=1)=0.3, P(X=2)=0.7)

E(X) = (1 * 0.3) + (2 * 0.7) = 1.7

E(x + y) if E(x) = 7.5, E(y) = 7.5

E(x + y) = E(x) + E(y) = 15

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Random variable example

A variable whose value is a numerical outcome of a random phenomenon.

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ગુણાત્મક સંબંધ Q = 0.5

જ્યારે બે ગુણધર્મો A અને B વચ્ચેનો ગુણાત્મક સંબંધ 0.5 થાય છે, ત્યારે તેનો અર્થ છે કે બંને ગુણધર્મો એકબીજાથી સ્વતંત્ર નથી.

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lim x → 1 નો અર્થ શું છે?

lim x → 1 નો અર્થ એ છે કે x ની કિંમત 1 ની નજીક આવે છે, પણ કદાચ 1 નથી.

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યદૃચ્છ ચલનું ઉદાહરણ

યદૃચ્છ ચલ એ કોઈ યદૃચ્છ ઘટનાનું પરિણામ છે જે સંખ્યાત્મક મૂલ્ય ધરાવે છે. ઉદાહરણ તરીકે, ત્રણ વખત સિક્કો ઉછાળવા પર મળતાં પૂછડાની સંખ્યા.

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E(x + y) શોધો, જો E(x) = 7.5 અને E(y) = 7.5

E(x + y) = E(x) + E(y) છે, તેથી આપેલ ડેટામાં E(x + y) = 7.5 + 7.5 = 15.

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X નું પ્રતીક્ષા મૂલ્ય શોધો જો P(X=1) = 0.3 અને P(X=2) = 0.7

X નું પ્રતીક્ષા મૂલ્ય, E(X) = (1 * 0.3) + (2 * 0.7) = 0.3 + 1.4 = 1.7

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Study Notes

Question 10

  • Given Q = 0.5 for two variables A and B, determine the relationship between them.
  • Options: A and B are independent, A and B are dependent, A and B are partially positive, A and B are partially negative.

Question 11

  • Determine the meaning of lim x → 1.
  • Options: x = 1, x is close to 1, x is greater than 1, x is less than 1.

Question 12

  • Identify the example of a random variable from the given options.
  • Options: Height and weight, Number of heads when a coin is tossed three times, Number of accidents on a road, Sunrise in the east.

Question 13

  • Given E(x) = 7.5 and E(y) = 7.5, calculate E(x + y).
  • Options: 15, 7.5, 8, 0.

Question 14

  • Calculate the expected value (mathematical expectation) of a random variable X.
  • Given: X = 1 with probability 0.3, X=2 with probability 0.7.
  • Options: 0.17, 117, 1.7, 17.

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