Ziaul Haque

CHARACTERIZATION OF CONTINUOUS DISTRIBUTIONS THROUGH RECORD STATISTICS

Abstract. A family of continuous probability distribution has been char-acterized through the difference of two conditional expectations, condi-tioned on a non-adjacent record statistic. Also, a result based on theunconditional expectation and a conditional expectation is used to char-acterize a family of distributions. Further, some of its deductions are alsodiscussed. 1. IntroductionLet ( X n ,n ≥ 1) be a sequence of independent, identically distributed contin-uous random variables with the distribution function ( df ) F ( x ) and the prob-ability density function ( pdf ) f ( x ). Let X u ( s ) be the s -th upper record value.Then the conditional pdf of X u ( s ) given X u ( r ) = x, 1 ≤ r 0 ,n ≥ m + 1 if and only if the distributionis exponential. Further, Lee et al. ([4]) have extended it and showed that

Morphological and biochemical responses of selected germplasm of tobacco to soil inoculation with Pythium aphanidermatum

The effect of inoculation with Pythium aphanidermatum was studied on total phenol (TP), salicylic acid (SA), chlorophylls and carotenoid contents of leaves and plant growth characteristics of five tobacco cultivars, namely RK-10 P3, RK-12 P3, RK-13 P4, RK-18 P8 and RK-26 P3, to assess cultivar response at biochemical and morphological levels. Root rot measured at 0–5 scale was 2.66 on cv. RK-10 P3, followed by 2. 33 on cv. RK-18 P8, 1.33 on cv. RK-26 P3 and 1.0 on cv. RK-13 P4. The cv. RK-12 P3 did not develop measurable root rot. The rhizosphere population of root rot fungus increased over time, being highest on the cv. RK-10 P3 (P ≤ 0.001), followed by cvs. RK-18 P8, RK-26 P3, RK-13 P4 and RK-12 P3. Inoculation with the fungus resulted in 5% (cv. RK-10 P3), 10.3% (cv. RK-18 P8, P ≤ 0.05), 10.9% (cv. RK-26 P3, P ≤ 0.05), 16.4% (cv. RK-13 P4, P ≤ 0.01) and 41.5% (cv. RK-12 P3, P ≤ 0.001) increase in the TP content of leaves. SA concentration in tobacco leaves increased marginally (0.8%–3%) in cvs. RK-10 P3, RK-18 P8 and RK-26 P3, but considerably (16%–17%, P ≤ 0.01) in cv. RK-13 and RK-12 P3 in comparison to uninoculated plants. Total chlorophyll content of leaves in response to inoculation with P. aphanidermatum decreased by 27% and 23% in tobacco cvs. RK-10 P3 and RK-18 P8 (P ≤ 0.001) and 17.6 (P ≤ 0.01) and 10.6% (P ≤ 0.05) in cv. RK-26 P3 and RK-13 P4, respectively. Reduction in chlorophylls a and b was 20% and 15% in cv. RK-10 P3 and 20% and 11% in cv. RK-18 P8. Total carotenoid contents of tobacco leaves decreased significantly in cvs. RK-10 P3 and RK-18 P8 (P ≤ 0.05). Significant and greater decrease in plant growth variables was recorded in the cultivars in which increase in TP and SA was lower and decrease in chlorophyll and carotenoids was greater. This study has revealed that greater synthesis of TP and SA may provide resistance in tobacco plants against P. aphanidermatum. The cv. RK-12 P3, in which greatest increase in the SA (17%) and TP (41.5%) was recorded, did not exhibit a significant decrease in plant growth variables and leaf pigments (P ≤ 0.05).