An approximation for P(X 2 + Y 2 ≤ K 2 σ 2 1 ) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ 2 1 and σ 2 2 and σ 1 ≥ σ 2 . Also, we provide asymptotic expressions for the probabilities for large values of β = K 2 (1 ‐ c 2 )/4 c 2 where c = σ 2 /σ 1 . These are illustrated by comparing with values tabulated by Harter [6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals.
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Z. Govindarajulu (1986) studied this question.
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