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Indian Navy SSR Probability & Statistics — practice questions

Explore 95 free Probability & Statistics questions in Indian Navy SSR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability & Statistics questions and exercises with answers

Showing questions 1–30 of 95.

For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:Read the answer and worked solution →E[X² + Y²] when X, Y are independent identically distributed with E(X) = 0, Var(X) = σ²:Read the answer and worked solution →At least one '6' in 4 throws of a fair die: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 →The angle 90° in radians is:Read 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

For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:

  1. $1$
  2. $0$
  3. $2.0$
  4. $1.25$
Show answer and solution

Correct answer: D. $1.25$

$F(0.5) = 3(0.5) - 2(0.5)^3 = 1.5 - 2(0.125) = 1.5 - 0.25 = 1.25$. (Note: this exceeds 1, which signals a problem with the source p.d.f. — but the question is purely about evaluating the given $F$ formula.)

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E[X² + Y²] when X, Y are independent identically distributed with E(X) = 0, Var(X) = σ²:

  1. 2σ²
  2. 2σ²
  3. σ²
  4. 0
Show answer and solution

Correct answer: B. 2σ²

E(X² + Y²) = E(X²) + E(Y²) = 2 × Var(X) (since E(X) = 0). = 2σ². (Used in chi-square distribution: sum of squares of standard normals.)

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At least one '6' in 4 throws of a fair die:

  1. 4/6
  2. 2/6
  3. 1 - (5/6)⁴ ≈ 0.518
  4. 2/3
Show answer and solution

Correct answer: C. 1 - (5/6)⁴ ≈ 0.518

Complementary: P(no 6 in 4) = (5/6)⁴ = 625/1296. P(at least one 6) = 1 - 625/1296 = 671/1296 ≈ 0.518.

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