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Mathematics and Statistics Flashcards

6 cards from real EIT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Mathematics and Statistics flashcards as text

  1. What is the solution to the first-order ODE dy/dx = 2y with y(0) = 3?

    Answer: y = 3e^(2x)

    Separating variables and integrating gives y = Ce^(2x); applying y(0)=3 yields C=3, so y = 3e^(2x).

  2. A normal distribution has mean 50 and standard deviation 10. What percentage of data falls within one standard deviation?

    Answer: 68%

    The empirical rule states approximately 68% of data falls within ±1 standard deviation of the mean.

  3. Which method is used to solve a system of linear equations by converting the augmented matrix to row echelon form?

    Answer: Gaussian Elimination

    Gaussian Elimination uses row operations to transform the augmented matrix into upper triangular form, enabling back substitution.

  4. The inverse Laplace transform of 1/s² is:

    Answer: t

    The inverse Laplace transform of 1/s² is t, since L{t} = 1/s².

  5. What is the probability that a standard normal variable Z is less than 1.96?

    Answer: 0.975

    From standard normal tables, P(Z < 1.96) ≈ 0.975, leaving 2.5% in the upper tail.

  6. Which test is used to determine whether sample data follows a specific distribution?

    Answer: Chi-square goodness-of-fit test

    The chi-square goodness-of-fit test compares observed frequencies with expected frequencies from a hypothesized distribution.