alleryStart learning →For random variable X uniform on [0, 1]: E(X²) =
- 0.5
- 1/4
- 1/2
- 1/3 (∫₀¹ x² dx = 1/3)
Show answer and solution
Correct answer: D. 1/3 (∫₀¹ x² dx = 1/3)
E(X²) = ∫₀¹ x² × 1 dx = 1/3. Var(X) = E(X²) - (E(X))² = 1/3 - 1/4 = 1/12.
Indian Navy Pilot Probability & Statistics — practice questions
Explore 75 free Probability & Statistics questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 75.
For random variable X uniform on [0, 1]: E(X²) =Read the answer and worked solution →The probability of getting an even number on a single throw of a die is:Read the answer and worked solution →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →Find the midpoint of A(2, −3) and B(8, 5).Read the answer and worked solution →Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Read the answer and worked solution →Match the trig identity to its resultRead the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →
Worked practice questions
The probability of getting an even number on a single throw of a die is:
- $\tfrac23$
- $\tfrac12$
- $\tfrac16$
- $\tfrac13$
Show answer and solution
Correct answer: B. $\tfrac12$
Even numbers on a die are {2,4,6}: 3 of 6 outcomes ⟹ 3/6 = 1/2.
The distance between the points $(1,2)$ and $(1,5)$ is:
- 6
- 3
- 5
- 4
Show answer and solution
Correct answer: B. 3
Same x, so distance = |5−2| = 3.
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