The probability density function 𝑓(𝑥) of a random variable 𝑋 which takes…
2026
The probability density function 𝑓(𝑥) of a random variable 𝑋 which takes real values is
Which one of the following statements is correct about the random variable 𝑋 ?
Answer: B. Normal — The standard normal-family density is f(x) = (1/(σ√(2π))) exp(-(x - μ)²/(2σ²)), for -∞ < x < ∞. The given density is (1/(3√(2π))) exp(-x²/18). Comparing terms…
- A.
Exponential
- B.
Normal
- C.
Poisson
- D.
Uniform
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Correct answer: B
The standard normal-family density is f(x) = (1/(σ√(2π))) exp(-(x - μ)²/(2σ²)), for -∞ < x < ∞. The given density is (1/(3√(2π))) exp(-x²/18). Comparing terms gives μ = 0 and 2σ² = 18, so σ² = 9 and σ = 3. Therefore X follows a normal distribution. The correct option is Normal.
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